Kinetic studies of gas-liquid reactions in capillary ......Declaration of Authorship I, Chara Psyrraki, declare that this thesis titled ‘Kinetics of gas-liquid reactions in capillary

Kinetic studies of gas-liquid

reactions in capillary

microreactors

by

Chara Psyrraki

Department of Chemical Engineering

University College London

February 2015

A thesis submitted for the degree of Doctor of Philosophy

Declaration of Authorship

I, Chara Psyrraki, declare that this thesis titled ‘Kinetics of gas-liquid

reactions in capillary microreactors’ and the work presented in it are my own

and have been generated by me as the result of my own original research.

Where information has been derived from other sources, I can confirm that

this has been clearly indicated in the thesis.

To my dad.

Page 4

Abstract

The main aim of this study was to develop a rate expression for the first

stage reaction for the production of methyl methyl acrylate (methyl ester of

methacrylic acid or MMA) using Lucite International Alpha Process. MMA is

an acrylic glass material which main features such as transparency, high

hardness, resistance to fracture and chemical stability makes it suitable for a

wide range of industrial applications. The first stage of the Alpha process is

the synthesis of methyl propionate (MeP) from ethylene, carbon monoxide

and methanol over homogenous Pd catalyst with selectivity higher than

99.9%. It is a gas-liquid catalytic reaction that takes place at high temperature

and pressure conditions. For the kinetic study of this system, experimental

studies were performed under a range of inlet conditions (temperature,

catalyst, gas and liquid inlet compositions) using capillary microreactors.

Moreover, a kinetic model for this system was developed and its validity

was verified by comparison with experimental results. Furthermore, a

reactor model was developed to simulate the reaction process and was

further used for parametric estimation of the kinetic model. For the

validation of the reactor model, experiments with a model system, a reaction

with well-studied kinetics were performed and the model predictions were

compared with the experimentally obtained results. For the complete

characterisation of the gas-liquid system, hydrodynamic study of the system

was conducted to identify the flow pattern, the void fraction and the mass

transfer characteristics of the system. Furthermore, hydrodynamic studies on

other gas-liquid systems were performed to investigate the effect of

parameters such as the gas-to-liquid ratio, the channel diameter and the fluid

properties on the hydrodynamic characteristics of the systems. Comparison

with previous hydrodynamic models was conducted and a new correlation

for the prediction of void fraction in gas-liquid systems under similar

conditions was suggested.

Page 5

Acknowledgements

This dissertation would not have been possible without the help of so many

people in so many ways.

First, I would like to express my deepest gratitude to my supervisor,

Professor Asterios Gavriilidis, for his full support, guidance and mentorship

throughout my study. I feel truly honoured of being one of his students.

Furthermore, I wish to express my sincere thanks to Lucite International and

specifically to Dr. Morris, Dr. Gobby, Dr. Tindale, Dr. Turner and Dr. Waugh

for the financial support, the insightful comments and the catalyst they

provided to carry out the experiments. Special thanks should be given to Dr.

Galvanin for his collaboration and help in my starting steps in the field of

kinetic modelling.

I also want to thank all my friends at UCL and especially Noor, Mithila,

Rema, Shade, Eria, Dave, Erik, Savio and Miguel for the time we spent

together in the office and the labs, our special tea and coffee breaks, the

Fridays at ULU and all the laughs. I will miss all of these a lot! I am also

very grateful to some very special friends of mine, Andrea, Ioli, Niki,

Aggelakos, Aggelica and Myrto who shared this journey with me with

inestimable support.

Above all I wish to thank my parents and my brothers for their faith in me,

their unconditional love, their endless support and understanding

throughout all these years. None of this would be possible without them and

to them I am eternally grateful.

Last but certainly not least, I would like to thank Aristotle for his constant

love, support, motivation, encouragement and patience at all times. He was

always cheering me up and stood by me through the good and bad times.

Page 6

Contents

Abstract ......................................................................................................... 4

Acknowledgements ................................................................................................. 5

Contents ......................................................................................................... 6

List of Figures ....................................................................................................... 11

List of Tables ....................................................................................................... 16

Nomenclature ....................................................................................................... 18

CHAPTER 1. Introduction & Background ..................................................... 21

1.1 Scope of Thesis ............................................................................................. 21

1.2 Methyl Methacrylate: Applications and Production Processes ............ 22

1.2.1 Background Information on Methyl Methacrylate ..................... 22

1.2.2 MMA Production Processes ........................................................... 23

1.3 Microreactors ............................................................................................... 26

1.4 Outline of Thesis .......................................................................................... 27

CHAPTER 2. Literature Review ....................................................................... 28

2.1 Kinetic Studies of Gas-Liquid Reaction Systems .................................... 28

2.1.1 Mass Transfer Models in Gas-Liquid Systems ............................ 29

2.1.2 Operational Regimes in Gas-Liquid Reactions ........................... 31

2.1.3 Hatta Number Criterion ................................................................. 33

2.2 Kinetic Studies in Capillary Reactors ....................................................... 33

2.2.1 What is a Capillary Microreactor? ................................................ 33

2.2.2 Advantages of Microreactors ......................................................... 36

2.3 Hydrodynamic Studies of Gas-Liquid Systems ...................................... 40

2.3.1 Flow Patterns in Microcapillaries .................................................. 42

2.3.2 Mass Transfer Studies of Gas-Liquid Reaction Systems in

Capillary Microreactors .................................................................. 44

Contents

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2.3.3 Void Fraction in Gas-Liquid Systems ........................................... 47

2.3.4 Experimental Techniques for Void Fraction and Residence

Time Distribution Studies .............................................................. 50

2.4 Homogeneous Catalysis: Methoxycarbonylation of Ethylene .............. 56

2.5.1 Carbonylation reactions in microreactors .................................... 56

2.5.2 Methoxycarbonylation of ethylene ............................................... 58

2.5.3 Proposed Mechanisms for Polyketones/Methyl Propionate

Formation .......................................................................................... 60

CHAPTER 3. Reactor Model Development and Validation ...................... 62

3.1 Introduction .................................................................................................. 62

3.2 Reaction System ........................................................................................... 62

3.2.1 Operating Conditions of Reaction System ................................... 64

3.2.2 Effect of Reaction Extent on Reaction Rate Constant ................. 66

3.2.3 Effect of Reaction Extent on Solubility of Carbon Dioxide ....... 68

3.3 Experimental Set-Up: Reaction and Analysis System ............................ 70

3.3.1 Reaction Quench .............................................................................. 73

3.3.2 Hydrodynamic Study of Gas-Liquid Flow .................................. 85

3.3.3 Residence Time Distribution Experiments .................................. 88

3.4 Reactor Model .............................................................................................. 92

3.4.1 Reactor Model Development ......................................................... 92

3.4.2 Comparison of Model with Experimental Results ..................... 99

3.5 Conclusions ................................................................................................ 103

CHAPTER 4. Hydrodynamic Study of Gas-Liquid Flow Systems in

Microcapillaries ........................................................................ 106

4.1 Introduction ................................................................................................ 106

Contents

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4.2 Experimental Set-Up and Operating Conditions ................................. 107

4.2.1 Residence Time Distribution Experiments: Method Analysis

and Validation ................................................................................ 110

4.3 Results ..................................................................................................... 112

4.3.1 Flow Patterns .................................................................................. 112

4.3.2 Residence Time Distribution Experiments ................................ 114

4.4 Conclusions ................................................................................................ 124

CHAPTER 5. Methoxycarbonylation of Ethylene: Set-up Design and

Preliminary Experiments ........................................................ 127

5.1 Introduction ................................................................................................ 127

5.2 Experimental Set-Up Design for Kinetic Experiments ........................ 128

5.3 Residence Time Distribution Studies under Reaction Conditions ..... 130

5.5 Analysis Methodology and Reactor Model ........................................... 133

5.6 Conclusions ................................................................................................ 136

CHAPTER 6. Kinetic Study of Methoxycarbonylation of Ethylene:

Experiments and Modelling .................................................. 138

6.1 Introduction ................................................................................................ 138

6.2 Experimental .............................................................................................. 139

6.2.1 Experimental Set-up ...................................................................... 139

6.2.2 Operating Conditions ................................................................... 141

6.3 Kinetic Experiments .................................................................................. 141

6.3.1 Dependence of Reaction Rate on Methanol Concentration ..... 141

6.3.2 Dependence of Reaction Rate on Ethylene Concentration ...... 143

6.3.3 Dependence of Reaction Rate on Carbon Monoxide

Concentration ................................................................................. 145

6.3.4 Dependence of Reaction Rate on Temperature ......................... 147

Contents

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6.4 Kinetic Modeling and Parameter Estimation ........................................ 149

6.1 Reaction Mechanism and Kinetic Models Discretisation ........ 149

6.2 Parameter Estimation .................................................................... 154

6.3 Sensitivity Analysis ....................................................................... 158

6.4 Information Analysis .................................................................... 160

6.5 Conclusions ................................................................................................ 162

CHAPTER 7. Conclusions & Future Developments .................................. 164

References ..................................................................................................... 171

Appendix A ..................................................................................................... 191

Calibration Graphs ............................................................................................. 191

Appendix B ..................................................................................................... 200

Photos of Experimental Set-Up ......................................................................... 200

Appendix C ..................................................................................................... 207

Experimental Data of Residence Time Distribution Experiments ............... 207

Appendix D ..................................................................................................... 217

Validation of RTD Method with Liquid Only Experiments ......................... 217

Appendix E ..................................................................................................... 219

Vapour-liquid Equilibrium and Reactor Models in gPROMS ..................... 219

Appendix F ..................................................................................................... 231

Fourier number calculation ............................................................................... 231

Appendix G ..................................................................................................... 232

Mass Balance Calculations during Blank Experiment................................... 232

Appendix H ..................................................................................................... 234

Fabrication of microseparators ......................................................................... 234

Appendix I ..................................................................................................... 235

Flow Observation ................................................................................................ 235

Appendix J ..................................................................................................... 237

Contents

Page 10

Supplementary technical data for Chapter 5 .................................................. 237

1. Standard operating procedure ..................................................... 237

2. Safety precautions ......................................................................... 239

3. Gas phase analysis ......................................................................... 240

4. Liquid phase analysis .................................................................... 245

5. Catalyst preparation and oxygen effect on catalyst

deactivation .................................................................................... 248

6. Reactor pretreatment section ....................................................... 252

7. Reactor design ................................................................................ 252

8. Separator design ............................................................................ 262

9. Tracer effect on RTD experiments ............................................... 263

10. Characterisation of the mass transfer characteristics of the

system .............................................................................................. 266

11. Vapour-liquid equilibrium model .............................................. 268

12. Conversion data for kinetic experiments of Chapter 5 ............ 273

Page 11

List of Figures

Figure 1.1 Methyl methacrylate downstream uses in a mature market. .................. 22

Figure 1.2 Global consumption of methyl methacrylate during 1980-2006............. 23

Figure 1.3 ACH process. ........................................................................................... 23

Figure 1.4 MAN Process. ......................................................................................... 24

Figure 1.5 Direct Oxidative Esterification Process. ................................................. 24

Figure 1.6 Isobutane process. .................................................................................... 25

Figure 1.7 BASF process. .......................................................................................... 25

Figure 1.8 Alpha Process. ......................................................................................... 25

Figure 2.1 Essential tools for kinetics determination of a reaction system ............... 28

Figure 2.2 Concentrations of reactants for an instantaneous (on the left) and for

a fast (on the right) reaction [8]. ................................................................................ 32

Figure 2.3 Concentrations of reactants for a slow (on the left) and for a very

slow (on the right) reaction [8]. ................................................................................. 32

Figure 2.4 General classification of flow patterns [93]. ............................................ 43

Figure 2.5 Photographs of gas-liquid flow patterns in a 1mm glass capillary

(from top left clockwise bubbly, slug and slug-annular, churn flow)[98]. ................ 44

Figure 2.6 Residence time distribution experiment based on an step-input

change [8]. .................................................................................................................. 52

Figure 2.7 Typical tracer response curve for ‘open vessels’ and relationship with

the dispersion number, 𝐷𝑢𝐿 [8]. ................................................................................ 54

Figure 2.8 Proposed mechanisms for the formation of polyketones and methyl

propionate. .................................................................................................................. 60

Figure 3.1 Effect of reaction extent on carbonate: bicarbonate ratio, 𝛽𝑐, along a

capillary reactor (L=1m, ID=0.5mm) for an initial 0.1M sodium carbonate:

bicarbonate (1:9) solution. ......................................................................................... 67

Figure 3.2 Effect of reaction extent on reaction rate constant, kr, along a

capillary reactor (L=1m, ID=0.5mm) when kr,0=0.0233 (T=10oC and βc=0.111). ... 68

Figure 3.3 Effect of carbon dioxide conversion on carbon dioxide solubility in a

carbonate-bicarbonate solution in a capillary reactor at 10oC. .................................. 70

List of Figures

Page 12

Figure 3.4 Schematic diagram of the experimental set-up for the study of the

carbon dioxide absorption in a carbonate-bicarbonate buffer solution. ..................... 71

Figure 3.5 Picture of the glass reactor (L=1m, ID=1mm) and the glass

microseparator where gas is being separated from the liquid and is analysed by

GC. ............................................................................................................................. 72

Figure 3.6 Schematic of open-phase gas-liquid separator. ........................................ 74

Figure 3.7 Schematic of the design characteristics (left) and photograph (right)

of the glass gas-liquid separator with a porous filter inside. ...................................... 75

Figure 3.8 Photograph (left) and schematic (right) of the silicon gas-liquid

microseparator with etching depth 300μm. ............................................................... 77

Figure 3.9 Schematic diagram of the experimental set-up for the test of the

performance of the glass microseparator (Mikroglas). ............................................... 78

Figure 3.10 Photograph of the microseparator when it was leaking from the

bottom of the silicon wafer with etching depth 480μm. ............................................. 79

Figure 3.11 Photograph of the glass gas-liquid microseparator (mikroglas). ........... 80

Figure 3.12 Technical drawing of the glass microseparator (Mikroglas) showing

its design characteristics ............................................................................................ 81

Figure 3.13 Operating conditions of the glass microseparator consisting of 80

capillaries, illustrating minimum applied pressure difference required to remove

all the liquid from the gas-liquid stream (grey line), applied pressure difference

at which gas breakthrough occurs (black line) and experimentally observed gas

(black dots) and liquid (grey dots) breakthrough. ...................................................... 84

Figure 3.14 Schematic diagram of the experimental set-up for flow observation

of the gas-liquid flow by means of a high-speed camera. ............................................ 85

Figure 3.15 Images of the glass circular tubing (ID=1mm) without water

medium (left picture) and with water medium (right picture) under

Fg=1.6ml/min and Fl=0.006ml/min). ........................................................................ 86

Figure 3.16 Schematic of experimental set-up for RTD study of model system. ...... 89

Figure 3.17 RTD curves for a range of gas-to-liquid ratios. ..................................... 90

Figure 3.18 A volume element ΔVℓ in the liquid phase in a gas-liquid reactor ........ 92

List of Figures

Page 13

Figure 3.19 A volume element ΔVg in the gas phase in a gas-liquid reactor. .......... 95

Figure 3.20 Conversion of carbon dioxide reaction against volumetric liquid

mass transfer coefficient for different liquid (Na2CO3:NaHCO3 (1:9)) flowrates

under constant gas (20% CO2) flowrate (Ug=0.1ml/min) at 10oC, at

atmospheric pressure in a capillary reactor with L=1m, ID=0.5mm. ....................... 98

Figure 3.21 Effect of liquid volume fraction on conversion of carbon dioxide

predicted from the model (Ug=0.1ml/min 20% CO2, Ul=0.02ml/min

Na2CO3:NaHCO3 (1:9) at 10oC) in a capillary reactor (L=1m, ID=0.5mm). .......... 99

Figure 3.22 Experimental results and model predictions for Fg=0.3-2ml/min,

Fl=0.03ml/min at 20oC in a glass reactor of 1m length and 1mm inner diameter

(No. experiments=1-4). ............................................................................................ 101


Fl=0.03ml/min at 10oC in a glass reactor of 1m length and 1mm inner diameter

(No. experiments=5-8). ............................................................................................ 101


Fl=0.03ml/min at 20oC in a glass reactor of 1m length and 0.5mm inner

diameter (No. experiments=9-12). ........................................................................... 102

Figure 3.25 Parity plot of carbon dioxide conversions for exps.1-12 (Table 3-8)

and model predictions. ............................................................................................. 103

Figure 4.1 Range of gas and liquid superficial velocities used in this study

compared to Triplett et al. [69]study in a 1mm circular capillary. ......................... 107

Figure 4.2 Schematic of the experimental set-up used for the hydrodynamic

study of gas-liquid systems in circular microcapillaries. ......................................... 108

Figure 4.3 Picture of the experimental set-up for the hydrodynamic study of

gas-liquid systems in circular microcapillaries. ....................................................... 109

Figure 4.4 Sensitivity of optical sensor to different components [177]. ................. 110

Figure 4.5 Flow model selection based on fluid properties, flow conditions and

vessel geometry [8]. .................................................................................................. 111

Figure 4.6 Observed flow patterns of the N2/DI water system at different gas-to-

liquid ratios (υg=0.2ml/min, υℓ=0.5ml/min on the left and υg=0.2ml/min,

List of Figures

Page 14

υℓ=0.005ml/min on the right) in a circular PFA capillary of 1mm inner diameter.

.................................................................................................................................. 113

Figure 4.7 Observed flow pattern of the N2/methanol system at different gas-to-

liquid ratios (υg=0.2ml/min, υℓ=0.5ml/min on the left and υg=0.2ml/min,


.................................................................................................................................. 113

Figure 4.8 Experimental F curves for different liquid flowrates (vl) at constant

gas flowrate (υg=0.2ml/min) for a N2/water system in a circular PFA capillary

of 1mm inner diameter. ............................................................................................ 115

Figure 4.9 Dispersion number for different liquid flowrates at 0.2ml/min gas

flowrate for a N2/water system in a circular PFA capillary of 1mm inner

diameter. ................................................................................................................... 116

Figure 4.10 Experimental F curves for N2/water (green line) and N2/10%

aqueous glycerol (blue line) at 0.3ml/min liquid flowrate and 0.2ml/min gas

flowrate in a circular PFA capillary of 1mm inner diameter. ................................. 118

Figure 4.11 Dispersion number against liquid flowrate for N2/water (blue line)

and N2/10% aqueous glycerol (red line) at 0.2ml/min gas flowrate in a PFA

circular capillary of 1mm inner diameter. ............................................................... 119

Figure 4.12 Experimental F curves of a N2/water system in PFA circular

capillaries of different inner diameters at 0.2ml/min gas flowrate and 0.1ml/min

liquid flowrate. ......................................................................................................... 120

Figure 4.13 Void fraction of N2/water against volumetric quality at 0.2ml/min

gas flowrate in circular PFA capillaries of 0.25, 0.5 and 1mm inner diameter. ...... 121

Figure 4.14 Fit of proposed correlation for the void fraction of N2/water systems

in circular PFA capillaries with inner diameter 0.25-1mm. ................................... 122

Figure 4.15 Void fraction of N2/water (blue line), N2/glycerol (green line) and

N2/methanol (orange line) against liquid flowrate at 0.2ml/min gas flowrate in a

circular PFA capillary of 1mm. ............................................................................... 123

List of Figures

Page 15

Figure 5.1 Schematic of the flow set-up for the kinetic study of

methoxycarbonylation of ethylene at elevated temperature and pressure

conditions. ................................................................................................................ 128

Figure 5.2 Simplified schematic of the experimental set-up for kinetic

experiments demonstrating the main points where gas and liquid composition

changes either because of temperature change (new VLE) or because of reaction. .. 134

Figure 6.1 Schematic of the flow set-up for the kinetic study of

methoxycarbonylation of ethylene at elevated temperature and pressure

conditions. ................................................................................................................ 139

Figure 6.2 Effect of methanol concentration on turnover frequency for a gas feed

stream of 10%v/v CO:C2H4 at 100oC, 10bara. ........................................................ 142

Figure 6.3 Effect of ethylene concentration on turnover frequency for a liquid

feed stream of 30%wt. MeOH:MeP and 10%vol. CO in the gas feed at 100oC,

10bara. ...................................................................................................................... 145

Figure 6.4 Effect of carbon monoxide concentration on turnover frequency for a

liquid feed stream of 30%wt. MeOH:MeP and 50%vol. C2H4 in the gas feed at

100oC, 10bara. .......................................................................................................... 146

Figure 6.5 Effect of temperature on turnover frequency for a liquid and gas feed

stream of 30%wt. MeOH:MeP and 10%vol.CO:C2H4 respectively at 10bara. ...... 148

Figure 6.6 Palladium-Hydride catalytic cycle for the formation of methyl

propionate. ................................................................................................................ 149

Figure 6.7 Parity plot of experimental and predicted from the kinetic model

reaction rate data. ..................................................................................................... 156

Figure 6.8 Sensitivity analysis of parameters theta1, theta2 and theta3 on

reaction rate.............................................................................................................. 159

Figure 6.9 Design Criteria for model-based design of experiments. ....................... 161

Figure 6.10 Information analysis of performed experiments based on Fischer

information. .............................................................................................................. 162

Figure 7.1 Process diagram for a design of experiments process. ........................... 170

Page 16

List of Tables

Table 2-1 Studies of gas-liquid reactions in microreactors in the literature. .. 34

Table 2-2 Studies of two-phase flow in micro and mini-channels in the

literature. .................................................................................................................. 40

Table 2-3 Void fraction correlations for gas-liquid systems. ............................ 48

Table 3-1 Reaction rate constant k (s-1) under different temperature

conditions, T (oC), and ratios of carbonate to bicarbonate concentrations,

βc. ............................................................................................................................... 65

Table 3-2 Stoichiometric table of the reaction in the capillary reactor. ........... 66

Table 3-3 Values of Sechenov constants ih and gh at 298K [153]. ................... 69

Table 3-4 Operating conditions of the glass microseparator test and

observations. ............................................................................................................ 81

Table 3-5 Conditions and results of flow observation and calculation of

mass transfer coefficient, kℓα and Hatta number at 0.03ml/min liquid

flowrate. .................................................................................................................... 86

Table 3-6 Results of RTD experiments for various gas-to-liquid ratios

conditions. ................................................................................................................ 90

Table 3-7 Model parameters and relevant correlations ..................................... 97

Table 3-8 Experimental results of the model reaction and corresponding

model predictions under different operating conditions when inlet liquid

flowrate was constant at 0.03ml/min................................................................. 100

Table 4-1 Physical properties of working fluids ............................................... 109

Table 5-1 Gas and liquid flowrates at reactor’s conditions (100oC, 10bara)

for the different cases tested. ............................................................................... 132

Table 5-2 Results of RTD experiments for different gas-liquid ratios. .......... 132

Table 6-1 Experimental conditions for the methanol series experiments. .... 142

Table 6-2 Experimental conditions for the ethylene series experiments. ...... 144

Table 6-3 Experimental conditions for the carbon monoxide series

experiments. ........................................................................................................... 146

List of Tables

Page 17

Table 6-4 Experimental conditions for the temperature series

experiments. ........................................................................................................... 148

Table 6-5 Estimation results of parameters of kinetic model. ......................... 157

Table 6-6 Estimation results of original parameters of kinetic model. .......... 158

Page 18

Nomenclature

Symbol Name Unit

A Interfacial area or

Numerical prefactor cm2

C Concentration mol/ml

Cp Specific heat kg/s

D

Diffusion coefficient or

Dispersion coefficient or

Diameter

cm2/s

cm2/s

cm

d density kg/ml

F Molar Flowrate mol/min

H

Solubility or

Fisher information matrix

mol/(ml∙atm)

h Heat transfer coefficient W/m2K

He Henry’s constant -

ID Inner diameter cm

j Superficial velocity cm/min

k

Reaction rate constant or

Thermal conductivity

s-1

W/m∙K

K Equilibrium constant -

kℓ Mass transfer coefficient

L Length cm

m Mass kg

N Moles or

Number of data

mol

-

Nomenclature

Page 19

n Viscosity Pa∙s

OD Outer diameter cm

P Pressure bar

p Perimeter cm

Q Sensitivity matrix

R Gas constant ml∙atm/K∙mol

r Reation rate

s Standard deviation

T Temperature oC or K

t Time min

TOF Turn over frequency mol/mol∙min

V Volume ml

X conversion -

x Liquid fraction or

Distance

-

cm

y Gas fraction -

Z Compressibility factor

Greek Symbols

α Interfacial area cm2

β

Carbonate-to-bicarbonate ratio or

Volumetric quality

-

-

γ Surface tension or

Activity coefficient

N/m

-

δ Film thickness μm

ε Void fraction -

Nomenclature

Page 20

θ Dimensionless time or

Model parameters -

μ Viscosity Pa∙s

π Pi number -

ρ Density kg/ml

τ Residence time min

υ Volumetric Flowrate ml/min

φ Fugacity coefficient -

Dimensional Numbers

D/uL Vessel dispersion number

Ha Hatta number

Nu Nusselt number

Pe Peclet number

Subscripts

0 Initial

c Cross sectional or Critical

cal Calculated

D Diameter

exp Experimental

f Final

g Gas

ℓ Liquid

ov Overall

s saturated

v vapour

Page 21

CHAPTER 1. Introduction & Background

1.1 Scope of Thesis

The scope of the thesis is to study the kinetics of the first stage reaction for

the production of methyl methacrylate (MMA) using Lucite International

Alpha Process. The first stage of the Alpha process is the synthesis of methyl

propionate (MeP) from ethylene, carbon monoxide and methanol over

homogenous Pd catalyst with selectivity higher than 99.9%. It is a gas-liquid

catalytic reaction that takes place at high temperature and pressure

conditions. The kinetic study will involve understanding of the effect of

reactant’s and catalyst concentrations as well as of temperature on reaction

rate. The main aim of this study is a rate expression for the

methoxycarbonylation of ethylene that is valid over a range of experimental

conditions.

In order to develop fundamental process knowledge accurate kinetic data are

essential. For this purpose, a capillary microreactor will be utilised for this

study as due to the advantages of microreactor technology it is believed that

it will produce accurate kinetic data. Moreover, mathematical models will be

developed to simulate the reaction process and used further for parameter

estimation. Aim of this project is to address all the phenomena included in

this process such as hydrodynamic aspects and vapour-liquid equilibrium.

Finally, this study will act also as a validation of the integrated microreactor

technology that will be developed for kinetic studies, so in the future kinetic

evaluation of other reactions of this nature will be able to be performed in

this system with confidence.


Page 22

1.2 Methyl Methacrylate: Applications and Production

Processes

1.2.1 Background Information on Methyl Methacrylate

Methyl methacrylate (MMA) is a very important and industrially interesting

monomer with excellent transparency, strength and outdoor durability. It is

an essential for the production of acrylic-based products with wide range of

applications from resins, coatings, adhesives to work surfaces and

automotive lights to signage, baths, and to dental prostheses and other

medical diagnostics equipment (Figure 1.1). Moreover it is a very

environmental friendly chemical due to its unique and cost effective

recycling capability.

Figure 1.1 Methyl methacrylate downstream uses in a mature market.

Another very exciting feature of the MMA market is the increasing level of

global growth. MMA demand has grown year-on-year over decades (Figure

1.2) at a rate that is well above the global GDP and is currently

approximately 3 million tes/annum.


Page 23

Figure 1.2 Global consumption of methyl methacrylate during 1980-2006.

1.2.2 MMA Production Processes

Over the years several routes were investigated for MMA production with

feedstock ranging from hydrogen cyanide, isobutylene, tert-butanol,

isobutene and ethylene.

The first process to produce methacrylic resin was introduced by Rohm &

Haas in 1933. Then, ICI developed and commercialised the ACH process

(Figure 1.3) in 1937. It starts form acetone and acetone cyanide and proceeds

via dehydration, hydrolysis and esterification. The ACH process was

actually the only industrial method for the production of MMA until 1982

and still is the predominant one in Europe and the U.S. accounting for

roughly 80% of world’s total MMA capacity.

Figure 1.3 ACH process.

However, it is a very high energy and capital demanding process due to the

intensive acid recovery and regeneration. Furthermore, there are also

environmental concerns related to this process due to the cyanide handling

and the great acid waste it produces.


Page 24

An improvement of the ACH process was suggested by Mitsubishi Gas

Chemicals in 1997 that solved the cyanide problem and waste problem.

However, this process involves a large number of reaction steps and

consequently an even larger number of energy demand due to the separation

and purification required in each step.

In 1984 Asahi Chemical developed a different route to produce MMA,

through methacylonitrile using isobutylene as raw material (Figure 1.4).

Figure 1.4 MAN Process.

However, this process presents disadvantages such as large waste due to the

production of ammonium bisulfate and use of ammonium that make the

process unattractive.

Asahi Chemical developed then the direct oxidative esterification process, a

process that does not produce ammonium bisulfate as a by-product. It is a

two-stage gas-phase oxidation followed by esterification (i-C4 route). In this

case the raw material is isobutylene or tert-butanol (Figure 1.5).

Figure 1.5 Direct Oxidative Esterification Process.

The main disadvantage of this process appears to be the large amount of

energy needed for separation of by-products.

This process was first studied by Rohm & Haas and after that by Asahi

Chemical, Sumitomo Chemical and Mitsubishi Rauon. It is the only method

that does not use unsaturated hydrocarbons as the raw material and

produces methacrylic acid one step (Figure 1.6).


Page 25

Figure 1.6 Isobutane process.

However, low catalyst’s selectivity (~70%) makes this process still not

possible commercially.

This process was developed and was commercialised by BASF in 1989 using

ethylene as a raw material using a homogeneous rhodium catalyst. It

involves the hydroformulation of ethylene to propionaldehyde,

condensation with formaldehyde to methacrolein, followed by oxidation and

esterification. The main drawback of this process is having to go through

methacrolein as an intermediate because of the high cost of methacrolein

oxidation.

Figure 1.7 BASF process.

Lucite International has invented a new two-stage process for the

manufacture of methyl propionate via carbonylation and esterification of

ethylene to methyl propionate which is then reacted with formaldehyde

under almost anhydrous conditions to form methyl methacrylate (Figure 1.8)

[1].

Figure 1.8 Alpha Process.

This technology was first demonstrated commercially in 2008 with a 100

kte/annum plant in Singapore and currently is the only existing technology


Page 26

that can compete the ACH process economically and in terms of production.

Unlike traditional MMA processes there are no polymer/solids blockage,

corrosion or machine issues or vulnerabilities and can cut the cost of making

MMA by 40%.

1.3 Microreactors

Advances in microfabrication techniques have allowed the rapid evolution

of microtechnology, widening the chemical engineering toolbox with devices

with feature sizes in the submillimeter range [2,3]. Nowadays, most process

equipment available in large scale has also been redesigned and studied in

the microscale, from micro-mixers and microreactors to microseparators and

microdistillation columns.

Microreactors have attracted increasing interest the last two decades due to

their unique features that create the potential for high performance

chemicals and information processing. These include high mass and heat

transfer rates due to the high surface-to volume ratio they provide, allowing

the kinetic study of traditionally mass transfer limited, highly exothermic

reactions but also high temperature and pressure processes with great

accuracy and safety. Furthermore, due to their significantly smaller volume

compared to conventional reactors, they provide a more controlled and

hence safer environment for the study of reactions containing poisonous and

hazardous components. Moreover, their small volume results also to more

economical processes as smaller chemical amounts are required, crucial

when handling very expensive or difficult to produce chemicals. Due to their

significant advantages, microreactors have been widely used the last decade

for chemical kinetic studies, chemical synthesis, process development and

new chemistry discovery in general by widening the window of operating

conditions and increasing the rate of information generation.


Page 27

1.4 Outline of Thesis

The thesis consists of seven chapters. In Chapter 2 literature relevant to the

thesis is reviewed. Topics include operational regimes in gas-liquid

reactions, benefits and kinetic studies in microreactors, hydrodynamic

studies of gas-liquid systems in microchannels (flow pattern, mass transfer,

void fraction, dispersion, etc.), homogenous catalysis and

methoxycarbonylation of ethylene. Chapter 3 focuses on the development of

a mathematical model to simulate the capillary reactor used in the study. The

reactor model will be a powerful tool in the kinetic study of the

methoxycarbonylation of ethylene. Validation of the reactor model was

conducted with experiments with a model reaction, a system with well-

studied kinetics. In Chapter 4 hydrodynamic studies of gas-liquid systems in

microcapillaries are presented and the effects of gas-to-liquid ratio, fluid

properties and channel size on the dispersion and the void fraction of the

system are studied. Comparison of void fraction results with previous

hydrodynamic models is shown and a new void fraction correlation is

suggested. Chapter 5 reviews the set-up design, the analysis methodology

and the catalyst preparation methodology for the study of

methoxycarbonylation of ethylene. Moreover, the hydrodynamic

characteristics of the system are investigated based on residence time

distribution experiments performed under reaction conditions. Also,

considerations on the vapour-liquid equilibrium of the system are presented.

Chapter 6 focuses on the kinetic study of the methoxycarbonylation of

ethylene and the effect of reactants’ concentrations and temperature on the

reaction rate is studied. Furthermore, a kinetic model that can fit all the

experimental data of the system is suggested and parameter estimation is

performed. Finally, in Chapter 7 the conclusions of the thesis are

summarised and recommendations for future work are given.

Page 28

CHAPTER 2. Literature Review

2.1 Kinetic Studies of Gas-Liquid Reaction Systems

Gas-liquid reactions are a substantial sector of chemical reaction engineering

and occur in many fields of experimental science. The kinetics of a chemical

reaction can be described by the rate expression of the reaction that can

explain adequately what parameters (i.e. concentrations of reactants,

temperature) affect the rate of that reaction and in which extent each of these

parameters affect the rate of the reaction. Knowledge of the kinetics of a

reaction can result to a number of benefits. Firstly, it allows the optimisation

of the reaction conditions which could lead to the decrease of the required

feedstock and the energy needs of that reaction. In addition, information on

the kinetics of a reaction system is essential when designing a reactor for that

reaction system. Optimal reactor design can result to the decrease of the

capital cost of a process. Hence, studying the kinetics of a reaction system

has the potential to significantly increase the profitability of the specific

process.

There are three main components that are essential for the kinetic study of

any reaction system (Figure 2.1). A first very important tool for a kinetic

study is a reactor model, a mathematical model that can describe the

phenomena taking place in the reactor. Next, a kinetic model for the system

is needed to describe the mechanism of the reaction and depict the effect of

various parameters on the reaction rate.

Figure 2.1 Essential tools for kinetics determination of a reaction system

Reactor Model

Kinetic Model

Kinetic Data

Kinetics


Page 29

Finally, kinetic data of the reaction are required; data that will depict

experimentally the effect of various parameters. The kinetic results are then

compared with the proposed kinetic model in order to find the rate

expression that fits satisfactorily all the experimental results. This

comparison between the experimental data can be done by means of a

reactor model.

Two are the most common methods for the analysis of kinetic data for the

determination of the rate equation of a reaction; the initial rates method and

the integral method. The initial rates method involves measurement of the

reaction rates at very short times before any significant changes in

concentration occur. This is particularly challenging in some cases, for

example when studying reactions with long induction time; parallel

reactions occurring at different rates. However, it is a simple method and its

most important advantage is that the reaction order found is the true order

without the influence from product inhibition or autocatalytic phenomena.

Another very popular method is the integral method which is an easy

method to use when testing particular mechanisms or simple rate

expression. In this method, a particular rate equation is evaluated by

integrating it and comparing the predicted curve (concentration, reaction

rate, time) to the experimental observations.

2.1.1 Mass Transfer Models in Gas-Liquid Systems

In multiphase reactions in order to ensure that the collected data are intrinsic

kinetic data and hence the reaction does not suffer from mass transfer

limitations, hydrodynamic study of the system is essential. A chemical

reaction can be either under mass transfer or kinetic control, depending on

the relative values of the corresponding mass transfer rate and reaction rate

of the reaction. For the kinetic study of a reaction system it is generally

preferable the reaction to be under kinetic control, without any mass transfer

resistances. It is also possible to study the kinetics of a reaction that is mass


Page 30

transfer limited but then the corresponding model will be more complicated

[4], as it should also take into account the mass transfer gradients into

account.

Consequently, the first step of a kinetic study, is to ensure that the there are

no mass transfer limitations. Several hydrodynamic models are available in

the literature [5,6] to describe the mass transfer in the gas-liquid interface.

The three most common mass transfer models are the film model, the Higbie

and the Danckwerts penetration model.

The film model is the simplest and the oldest one and it assumes that near to

any fluid interface there is a stagnant film of thickness 𝛿 through which the

transport process takes place by simple molecular conduction, while the

conditions outside this film, in the bulk of the phase are assumed to be

constant. The mass transfer coefficient for physical absorption, 𝑘ℓ𝑜 is

expressed by (2.1),

𝑘ℓ

𝑜 =𝐷ℓ

𝛿 (2.1)

where Dl is the molecular diffusivity of the absorbing component in the

liquid. The film model theory does not give any valuable information for the

process. Usually it is used as a first reasonable guess or in problems that

have already a lot of mathematical difficulties and they can be solved only

using this model.

The Higbie’s penetration model is based in the hypothesis that the gas-liquid

interface is made up of a variety of small liquid elements, which are

continuously brought up to the surface from the bulk of the liquid and vice

versa by the motion of the liquid phase itself. Each element of liquid, as long

as it stays on the surface, may be considered to be stagnant, and the

concentration of the dissolved gas in the element may be considered to be

everywhere equal to the bulk-liquid concentration when the element is

brought to the surface. Therefore, mass transfer takes place by unsteady

molecular diffusion in the various elements of the liquid surface.


Page 31

Furthermore, another assumption of this model is that all the surface

elements stay at the surface for the same amount of time * / bt d u , where d

is the length of the bubble and ub its velocity. The mass transfer coefficient

for physical absorption, 0

lk is expressed by (2.2),

𝑘ℓ

𝑜 = 2√𝐷ℓ

𝜋𝑡∗ (2.2)

The difference between Higbie’s and Danckwerts’ model is that the latter

assumes that the probability for a surface element to disappear from the

surface in a given time interval is independent of its age. In this case, the rate

of disappearance of surface elements is simply proportional to the number of

elements of that age which are present. The mass transfer coefficient for

physical absorption, 𝑘ℓ𝑜 is expressed in this case by (2.3),

𝑘ℓ

𝑜 = 2√𝐷ℓ

𝑡𝐷 (2.3)

where tD is an equivalent diffusion time and may be regarded as an average

life of surface elements [5].

2.1.2 Operational Regimes in Gas-Liquid Reactions

In multiphase reaction systems mass transfer is a crucial phenomenon,

leading the two phases to come into contact and afterwards to react. When

considering a reaction between a gas (A) and a liquid (B) is considered,

where the gas is soluble in the liquid while the liquid cannot enter the gas,

the overall rate expression for this reaction should consists of both the mass

transfer resistances and the resistance of the chemical reaction. Also, in this

system, using the two film theory, there are two mass transfer resistances, in

the gas film and in the liquid film [7]. Consequently, there are four main

regimes, from instantaneous to very slow reaction. There are also some

intermediate regimes, but here only the main regimes will be described [8].


Page 32

For an instantaneous reaction, the mass transfer in the gas film is the rate

controlling step and when the gas reaches the gas-liquid interface reacts

instantaneously as it is shown in Figure 2.2.

Figure 2.2 Concentrations of reactants for an instantaneous (on the left) and for a fast (on the right) reaction [8].

For a fast reaction the diffusion of the gas into the gas and the liquid film is

slow, but when the gas comes in contact with the gas-liquid interface does

not react instantly. However reaction is fast enough and the gas reacts

completely within the liquid film, as it is shown in Figure 2.2.

In Figure 2.3 (on the left) the case of a slow reaction appears where the

reaction takes place in the main body of the liquid, while the two films still

provide a resistance to the gas to transfer into the liquid bulk.

Figure 2.3 Concentrations of reactants for a slow (on the left) and for a very slow (on the right) reaction [8].

For a very slow reaction, the mass transfer limitations are negligible and

therefore the concentrations of the gas and the liquid are uniform in the

liquid. The reaction takes place in the bulk of the liquid as it is shown in

Figure 2.3 (on the right) and is the rate controlling step. Consequently, the

overall rate expression of the reaction is determined by the kinetics alone.


Page 33

The criterion to identify in which regime a reaction system operates is by

calculating Hatta number.

2.1.3 Hatta Number Criterion

For a pseudo-first order reaction gA B C , assuming that the gas film

resistance is negligible, the definition of the dimensionless Hatta number is

expressed by (2.4),

𝐻𝑎 =

√𝑘𝑟 ∙ 𝐷𝐴ℓ

𝑘ℓ (2.4)

where 1( )rk s is the reaction rate constant of the reaction, 2( )AlD m s is the

reactant A diffusivity into the liquid and ( )lk m s the mass transfer

coefficient of A in the liquid phase.

The strict definition of Hatta criterion is that if Ha<<0.03 the reaction takes

place into the bulk of the liquid [6,8-10] as it is shown in Figure 2.3 (on the

right) where there are no mass transfer limitations (no concentration

gradients of the gas into the liquid). However, many researchers have also

studied the kinetics of reactions, assuming negligible mass transfer

limitations, for Ha<<0.3 [11-13]. Concluding, although the strict criterion for

the kinetic control of a reaction is when Ha<<0.03, at Ha up to 0.3 the

reaction rate is not limited by mass transfer processes. Above this value

Ha>0.3, mass transfer begins to influence the reaction rate as it is shown in

Figure 2.2 (on the left) and surface area is the controlling rate factor.

2.2 Kinetic Studies in Capillary Reactors

2.2.1 What is a Capillary Microreactor?

When the technology that was needed to produce structures at micro-scales

was developed, new designs of fluid flow systems on the micro-scale were

opened up. Nowadays, microreactors with very small, down to few tens of

microns, channel internal diameters can be produced by a variety of


Page 34

manufacturing techniques, allowing the use of them. Capillary microreactors

are the simplest kind of microreactors as they are just capillaries whose

internal diameter ranges from some tens of microns to hundreds of microns.

Microreactors have been used in the past by many researchers for the study

of not only single phase reactions [14,15] but also liquid-liquid [16-18], gas-

liquid [11,19-32] (Table 2-1) and gas-liquid solid reactions [33-38] catalytic or

non-catalytic. Many reviews are available in the literature for the potential

and the challenges of microreactors [39-41].

Table 2-1 Studies of gas-liquid reactions in microreactors in the literature.

Author Reaction/ Conditions Reactor Design

Jähnisch [21]

(2000)

Fluorination of toluene/

T=-15- -42oC

Falling film microreactor

0.1mm x 0.3mm cross section,

Micro bubble columns

0.5mm x 0.5mm, 0.3mm x 0.1mm

Chambers [20]

(2001)

Fluorination of 1,3-

dicarbonyl substrates/

T=0-20oC

Nickel microchannel

0.5mm wide x 0.5mm deep

L=10cm

Natividad [23]

(2004)

Hydrogenation of 2-butyne-

1,4-diol/

Pd-Al, P=1-3bar, T=25-55 oC

Capillary monolith

ID=1mm and 2mm

L=15cm and 34cm

Basheer [42]

(2004)

Oxidation of glucose/

Gold(0), T=20oC

Glass capillary

5cm x 0.4mm

1. Önal [22]

2. (2005)

Hydrogenation of α,β-

unsaturated aldehydes/

Ru(II)-TPPTS,

P=10-20bar, T=60oC

PTFE capillary

ID=0.5, 0.75, 1.00 mm

L=3, 6, 12m

Ducry [31]

(2005)

Nitration of phenol/

T=5-60oC

Glass microchannel

10x0.5mm width

Enache [30]

(2005)

Resorcinol hydrogenation/

Rh/γ-Al2O3

T=100oC, P=6-10bar

Capillary

ID=3.86mm, L=50cm

Tsoligkas [24]

(2007)

Hydrogenation of 2-butyne-

1n4-diol/

Pd-Al, T=24-50oC

Ceramic capillary

ID=1.69mm, L=30cm

Enache [43]

(2007)

Resorcinol hydrogenation/

Rh-Al2O3, Pd-C

T=100oC, P=10bar

HEx reactor

1-2mm width


Page 35

Table 2-1 (continued)


Miller [28]

(2007)

11CO carbonylative cross-

coupling reactions/

Pd-complex, T=75oC

Teflon capillary

ID=1mm, L=45cm

Murphy [44]

(2007)

Aminocarbonylations of

3-iodoanisole,

morpholine, 4-

bromobenzonitrile/

Pd, T=98-160oC

P=4.5-14.8bar

Silicon-Pyrex

V=0.078-0.4ml

Wang [45]

(2009)

Oxidation of alcohols/

Au-Pd, T=50-70oC

Capillary reactor

ID=0.25mm, L=50cm

Rebrov [38]

(2009)

Hydrogenation of 2-

Methyl-3-butyne-2-ol/

Pd-TiO2,Pd25Zn75/TiO2

T=55-64 oC

Fused silica capillary

ID=0.25mm, L=10m

De Mas [46]

(2009)

Direct fluorination of

toluene

T=20oC

Silicon-Pyrex

Dh=0.215mm

L=20mm

Tsoligkas [25]

(2009)

Hydrogenation of 4-

nitrobenzoic acid/

Pd-Al, T=25oC

Alumina ceramic capillary

ID=1.69mm, L=30cm

Ng [26]

(2010)

Direct formation of

hydrogen peroxide/

Pd complex, T=25oC

Glass capillary

ID=0.5mm-2mm

Jetvic [27]

(2010)

Cyclohexane oxidation

with oxygen/

Cobalt naphthanate

T=160oC, P=15.2bar

Stainless steel capillary

ID=2.16mm, L=15m

Fischer [11]

(2010)

Oxidation of cyclohexane

with air/

P= 20-80bar, T=180-260oC


ID=0.5, 0.75, 1.00, 2.15 mm

L=0.6-8.3 m

Protasova [29]

(2011)

Hydrogenation of citral

(3,7-dimethyl-2,6-

octadienal)/

Au-TiO2, Pt-Sn-TiO2

T=65-75 oC

Silica capillary

ID=0.25mm, L=10m

Keybl [47]

(2011)

Hydroformulation of 1-

octene/HRhCO(PPh3)3,

T=85-105oC

P=25bar

Silicon-Pyrex

0.4 x 0.4mm cross section


Page 36



Tidona [48]

(2013)

CO2 hydrogenation,

Reverse water-gas shift,

CO hydrogenation/

Pt-CeO2, T=450-600oC

P=200-1000bar


ID=1mm

Al-Rawashdeh

[49] (2013)

Hydrogenation of

phenylacetylene/

[Rh(NBD)(PPh3)2]BF4]

(NBD = norbornadiene)

T=70oC, P=10bar

Barrier-based microreactor

1.23mm width x 1.23mm depth

L=2m

Liu [50]

(2013)

Oxidation of alcohols,

Conversion of aldehydes,

amines to amides/

Ru-Al2O3, T=80-130oC

Silicon-Pyrex channel

27 × 8 × 0.6mm3

Paunovic [51]

(2014)

Direct synthesis of

hydrogen peroxide/

Au-Pd, T=30-42oC

P=15-30bar

Capillary

ID=0.32mm, L=1m

Truter [52]

(2015)

Epoxidation of propene

with hydrogen peroxide/

Si-Ti, P=6bar, T=40oC

PEEk capillary

ID=0.9mm, L=350-595cm

2.2.2 Advantages of Microreactors

Initially, researchers started using capillary reactors with internal diameters

less than 1mm to study single phase reactions between two parallel fluid

streams where diffusion between them was taking place [14,15]. They

observed that one of the benefits of using channels with small diameters is

that the diffusion pathway is much smaller fact that enhances largely the

mass transfer rate [11,17-30,53]. It is well known that in a channel with

diameter on the sub-millimetre scale, the fluid flow is mainly laminar (due to

the small Reynolds numbers) and the main controlling factor in mass

transfer is diffusion. Furthermore, to assess the efficiency of mixing between

two fluids Fourier number, Fo, can be calculated, which relates the residence

time in the mixing chamber or reactor to the binary diffusion coefficient and

a characteristic length scale,


Page 37

2

D tFo

d

(2.5)

where D is the fluid diffusivity (m2s-1), t is the contact time (s) and d is path

length for diffusion (m), which concerning a reaction inside a capillary is its

internal diameter. Good mixing is achieved for Fo > 0.1 and complete mixing

for Fo > 1. Hence by decreasing the diffusion path length (e.g. by decreasing

the internal diameter of the capillary) to the micro-scale, complete mixing

can be achieved over time scales of few seconds, as the diffusivity of the

most liquids ranges between 10-9 m2s-1 to 10-8 m2s-1. Consequently, the

excellent mixing between two fluids is one of the first advantages researchers

observed in capillary microreactors.

Rapid development of microreactors for gas-liquid applications was

observed due to their benefits compared to conventional multiphase

reactors. Hessel et al. [21] studied the direct fluorination of toluene in

microreactors using bubbly or slug flow and observed that due to the high

interfacial surface area provided, the mass and the heat transfer were

significantly enhanced leading to an increase in conversion and selectivity in

microreactors compared to the laboratory benchmark. Gas-liquid interfacial

mass transfer is enhanced in microreactors due to the thinness of the liquid

film, leading to increased reaction rates for mass transfer limited reaction

[16,17,21,22,25,30]. In addition, enhanced mass transfer rates under slug flow

in microreactors was also attributed to the internal convective circulations

taking place inside the plugs due to the shear forces at the walls opposite to

the flow direction. Further increase in the average flow velocity was found to

increase the intensity of these internal circulations [54]. This enhancement of

mass transfer in microreactors leads to reaction performance better than that

provided by conventional multiphase reactors especially for mass transfer

limited reactions.

Due to the large interfacial area that microreactors provide, heat transfer is

also significantly enhanced. This feature allows reactions that in


Page 38

conventional reactors are taking place in mild conditions due to safety

reasons, to be performed in microreactors under much harsher conditions

[55]. For example, many researchers studied the direct fluorination of

aromatics in microreactors [19-21,56]. Those reactions are highly exothermic

and in conventional rectors (e.g. batch reactors) the safety issues regarding

the temperature control are very important especially on a large scale

leading to mild operating conditions. However, in microreactors where heat

transfer is largely enhanced, these reactions can take place isothermally even

under severe conditions leading to increased yields. This feature of

microreactors results also to less substrate degradation as well as increased

reaction selectivity.

The nitration of aromatics is another example illustrating how suitable

capillary reactors are for the study of highly exothermic reactions. Dummann

et al. [18] studied this liquid-liquid reaction isothermally into PTFE

capillaries with inner diameters 0.5 to 1mm. They reported that due to the

high specific area, the heat transfer was efficient enough to remove the

released heat by the exothermic reaction, allowing an isothermal operation.

Another benefit of capillary microreactors that they observed is the

formation of a stable two-phase plug flow pattern for the immiscible liquids,

which results to a uniform and well defined interfacial area and

consequently better control of the reaction.

Another noteworthy example of processes that have been benefited by the

development of microreactors is those that require extreme temperature and

pressure conditions such as the hydrogen peroxide. The direct catalytic

formation of hydrogen peroxide from hydrogen and oxygen requires

extreme and dangerous operating conditions such as high pressures.

However, the last years many researchers have demonstrated the possible

use of microreactors for the production of hydrogen peroxide [51,57-59].

Apart from reactions at extreme temperature and pressure conditions, other

reactions facilitated in microreactors are those with explosive, toxic or


Page 39

hazardous chemicals involved. This is because microreactors offer enhanced

safety compared to conventional reactors due to their small volumes. Typical

example is Maurya et al. [60] who used microcapillaries for multiple

reactions and separations of hazardous ethyl diazoacetate, one of the most

common diazocompounds and very industrially interesting compound in

fine chemicals and pharmaceutical production.

Moreover, another benefit of microreactors is the small reagents volumes

that require due to their small volumes. This feature is essential when the

reagents are very expensive or minimal amounts are available, often in fine

chemicals and pharmaceutical industries.

Another significant benefit of microreactors that was early recognised [61-64]

is the ease of transforming this microfluidic technology into an industrial

tool by numbering up (use of parallel reactors) instead of scaling up

(increase the characteristic dimensions of reactors) [53,65]. That’s because the

channel design that was used for the laboratory scale is the same as in the

industrial scale. The only thing that differs is the number of channels that are

needed to be used in parallel. In other words, scale up of microchannels is

achieved by simple replication and not by increasing the size of the process

unit [17]. Consequently, the development costs associated with the scale-up

methodology followed for conventional systems are dramatically decreased.

However, it should be noted that scaling out still involves challenges in inlet

flow distribution [66] and reaction monitoring methods.

In conclusion, the miniaturisation of chemical reactors has lots of

advantages, such as efficient mass and heat transfer, ability to operate at

high pressures, safety advantages of small volume usage and ease of scale

out. These advantages can largely be exploited from both academia by

producing essential chemical information [67] but also by industry by

achieving increased reaction rates and selectivity in a safer manner.


Page 40

2.3 Hydrodynamic Studies of Gas-Liquid Systems

Gas-liquid two phase flow in small channels has been studied extensively

the last decade [68-92]. This is due to the essential information it provides for

many applications, such as the design and the optimisations of heat

exchangers, multiphase reactors and other microstructured process units.

The hydrodynamic study of a multiphase system provides information

about the flow behaviour, the flow characteristics, the mixing quality and the

mass transfer characteristics of the system and is essential for the complete

understanding of any gas-liquid process. The hydrodynamics of multiphase

systems in microchannels present differences compared to larger systems

mainly due to the increased importance of surface over volume forces and

hence flow behaviour predictions that exist for larger systems cannot be

applied in smaller channels.

In Table 2-2 the studies available in the literature on two phase-flow systems

in micro and mini-channels are listed.

Table 2-2 Studies of two-phase flow in micro and mini-channels in the literature.

Author Experimental

Conditions

Findings

Barajas et al. [73] (1999)

Pyrex, polyethylene, polyurethane, FEP ID=1-9mm (C) Air/Water

For partial- wetting surfaces (θ<90o) contact angle has little effect on transition boundaries, while for non-wetting surfaces (θ>90o) they changed significantly

Fukano et al. [74] (1999)

ID=1.6mm (C) Air/Water

Flow direction does not affect significantly flow patterns

Coleman et al. [75] (1999)

Pyrex, Dh=1.3-5.5mm (C), (R) Air/Water

Channel diameter and surface tension affects the flow pattern and their transitions

Triplett et al. [69,76] (1999)

Pyrex, ID=1.1, 1.45mm (C) Dh=1.09, 1.49mm (T) Air/Water

Channel geometry has little effect on flow patterns transitions

Homogenous model predicts well pressure drop data except annular flow

Zhao et al. [77] (2001)

PMMA, Dh=0.866-2.886mm (T) Air/Water

Channel diameter affects flow transitions

Sharp corners affect flow patterns


Page 41


Author Experimental

conditions

Findings

Serizawa et al. [71] (2002)

Silica quartz, ID=20-100μm (C) Air/Water, Steam

Two phase flow patterns are sensitive to surface wettability and contamination

Kawahara et al. [78] (2002)

Fused silica, ID=100μm (C) Nitrogen/Water

Time-averaged void fraction based on images analysis

Pressure drop data were well correlated by Lockhart-Martinelli’s separated flow model.

Chen et al. [79] (2002)

Glass, ID=1, 1.5mm (C)

Modified drift flux model was suggested for void fraction and bubble velocity

Chung et al. [72] (2004)

Fused silica, ID=50-530μm (C) Nitrogen/Water

Channel diameter affects flow pattern transition lines

Void fraction deviated from Armand-type correlation

Slug flow model was proposed for the prediction of pressure drop

Chung et al. [80] (2005)

Fused silica, ID=100μm (C) Dh=96μm (R) Nitrogen/Water

Deviated from Armand correlation Lockhart-Martinelli’s separated flow

model estimated well pressure drop

Ide et al. [84] (2007)

ID=1-4.9mm (C) Dh=1-1.98mm (R) Air/Water

Effects of tube diameters and aspect ratios on flow parameters were studied

Flow frictional multiplier becomes very large compared to Chisholm’s prediction.

Correlations of holdup and pressure drop were proposed

Lee et al. [85] (2008)

Glass, Teflon, Polyurethane, ID=1.46-2mm (C) Air/Water, Methanol

Wet and dry flow patterns were identified

Warnier et al. [86] (2008)

Glass, D=100x50μm (R) Nitrogen/Water

Mass balance-based model was suggested for the prediction of void fraction and flow characteristics

Yue et al. [87] (2009)

PMMA, Dh=200-667μm (R) CO2/Water

Flow map was suggested plotted with Weber numbers

Separated flow model was used for the pressure drop estimation under churn, slug-annular and annular flow

Empirical correlation was proposed to describe mass transfer data under short film contact film condition


Page 42


C: circular, R: rectangular, T: triangular cross section of channel

2.3.1 Flow Patterns in Microcapillaries

When studying the hydrodynamics of a multiphase system, one of the most

important issues is the flow pattern that describes the spatial distribution of

the two phase flow in the channel. The importance of characterising the flow

pattern of a system lies mainly on the fact that depending on the flow pattern

the system presents different mass and heat transfer characteristics a

different pressure drop. Flow patterns of gas-liquid systems in

microchannels differ significantly to those in larger channels. This is mainly

due to the increased relative importance of surface forces over volume

forces. In addition, due to the small Reynolds numbers achieved in

microchannels, laminar flow is established, where viscous forces dominate

over inertial ones [93].

There are extensive studies on the characterisation of gas-liquid flows in

microchannels [69,78,81,82,93-97]. The flow pattern depends on several

Author Experimental

conditions

Findings

Saisorn et al. [88] (2009)

Fused Silica, ID=150μm (C) Air/Water

Pressure drop correlation was developed based on separated flow model with a modified two phase frictional multiplier

Kawahara et al. [89] (2009)

Fused Silica, ID=250μm (C) Nitrogen/Water, Aqueous ethylene solutions

Two phase friction multiplier was lower for the flows with contraction

Armand-type correlation could predict well the void fraction data

A two-fluid model correlation was also suggested for the void fraction estimation with modified interfacial friction force

Sur et al. [90] (2012)

Fused Silica, Dh=100-324μm (R) Air/Water

Flow pattern-based models provided the best prediction of two-phase pressure drop data

Wang et al. [91] (2014)

Glass, Polydimethylsiloxane, Dh=66.7-133.3μm (R) Air/Water

Mass transfer performance in microchannels with different surface properties was studied and mass transfer correlations were suggested with a factor of wall wettability included


Page 43

factors such as the gas and the liquid flowrates, the channel size and

geometry, the channel wettability by the certain fluid and the fluid

properties (e.g viscosity, density, surface tension)[93].

Typically, as the gas flowrate increases while keeping the liquid flowrate

constant the observed flow patterns range from bubbly to slug (also called

segmented or Taylor flow), churn, slug-annular and annular flow (Figure

2.4-Figure 2.5).

Figure 2.4 General classification of flow patterns [93].

Bubbly flow is often observed when the superficial velocity of the gas phase

is smaller than that of the liquid phase. The gas phase is dispersed as small

bubbles, and the diameter of each bubble is much smaller than the diameter

of the channel (Figure 2.5). When the gas and liquid phase velocities are

similar to each other, the volume equivalent diameter of gas bubble becomes

greater than the channel diameter, and liquid slugs are separated by the

bubbles. This mode of flow is called slug flow, Taylor flow or segmented

flow. At a high gas velocity, three different flow regimes may appear. In

churn flow, each gas slug is followed by many small gas bubbles. In annular

flow, the liquid forms a thin film on the inner wall. The gas phase flows

through the central part of the microchannel. Slug-annular flow is sometimes


Page 44

called Taylor-annular flow, and is similar to the annular flow, except that a

wave with large amplitude travels on the liquid surface.

Figure 2.5 Photographs of gas-liquid flow patterns in a 1mm glass capillary (from top left clockwise bubbly, slug and slug-annular, churn flow)[98].

2.3.2 Mass Transfer Studies of Gas-Liquid Reaction Systems in

Capillary Microreactors

An important advantage of microreactors compared to conventional process

equipment is the enhanced mass transfer rates they present principally due

to the increased interfacial areas they provide [99]. Evaluation of the mass

transfer characteristics is essential for the design of gas-liquid contactors as

depending on the relative rates of diffusion and reaction, the system may fall

into different reaction regimes. It has been reported that the mass transfer

characteristics of a reaction are largely influenced by the flow pattern [25] of

the system. Several authors [99-104] have studied the mass transfer

characteristics of multiphase systems in microreactors and have proposed

various correlations for the mass transfer coefficient mainly in slug flow

regime.

One of the oldest mass transfer studies in circular capillaries is of Bercic and

Pintar [102] who studied the absorption of methane in water using capillaries

of 1.5, 2.5 and 3.1mm diameter. They found that the mass transfer coefficient

is dependent on both gas and liquid superficial velocities and the length of

the unit cell length and proposed the following empirical correlation for

estimation of k for Taylor flow in capillaries,


Page 45

1.19

0.570.111

1

g

g UC

j jk

L (2.6)

where gj j are the gas and the liquid superficial velocities,

g is the gas

hold-up, and UCL is the unit cell length (length of one gas bubble and one

liquid slug). It is noteworthy that (2.6) does not show any dependence on the

capillary diameter. A possible reason for this is that Bercic and Pintar used

in their study relatively large unit cell lengths, where the liquid film reaches

saturation quickly and is not effective [101,103].

In contrast to the Bercic and Pintar approach, several authors [99-101,103-

105] considered that both the two hemispherical caps and the film side of the

bubble contribute to the mass transfer. van Baten and Krishna [105] used

computational fluid dynamics (CFD) simulations of mass transfer in circular

capillaries (1.5, 2, 3mm diameters) under Taylor flow. They showed that for

large diameters (2, 3mm) the deviation from the prediction of (2.6) is

remarkable and they developed a more fundamental model to describe the

mass transfer from Taylor bubbles for short (Fo<0.1) and long (Fo>1) contact

times.

In another study Vandu et al, [101] studied the mass transfer characteristics

in an air-water system for short contact times (Fo<0.1) between the liquid

film and the gas bubbles under Taylor using square and circular capillaries

of 1, 2 and 3mm diameter and they suggested the following correlation (2.7),

𝑘ℓ𝛼 = 4.5√

𝐷 ∙ 𝑗𝑔

∙ 𝐿𝑈𝐶

1

𝑑 (2.7)

where, D is the liquid phase diffusivity, 𝐿𝑈𝐶 is the unit cell length and d is

the capillary inner diameter.

For long contact times (Fo>1) between the liquid film and the gas bubbles,

the liquid film approaches saturation and therefore its contribution to the


Page 46

overall mass transfer rate becomes gradually negligible. A criterion to

identify whether the film contribution to the mass transfer is active or not

was developed by Pohorecki [106].

𝐿 𝐷

𝑢 𝛿2≪ 1 (2.8)

where L is the bubble length, D is the diffusivity, u is the bubble velocity and

𝛿 is film thickness.

The corresponding correlation of mass transfer coefficient for long contact

times (Fo>1) was proposed by van Baten and Krishna [105] in (2.9).

, ,

42 42 3.41

gBcap cap film film

UC film

Du Dk k k

d L d (2.9)

In a more recent study, Yue et al. [99] studied CO2 absorption into water, a

sodium carbonate/bicarbonate buffer solution and a sodium hydroxide

solution, in a horizontal rectangular microchannel with a hydraulic diameter

of 667µm. They proposed correlations for the mass transfer coefficient under

slug flow (2.10) and under slug-annular and churn flow (2.11).

0.213 0.937 0.50.084Re RegSh d Sc (2.10)

0.344 0.912 0.50.058Re RegSh d Sc (2.11)

where, Sh is the liquid Sherwood number, Reg and Re are the gas and the

liquid Reynolds number and Sc is the liquid Schmidt number. Yue et al.

[99] concluded that at a fixed superficial liquid velocity, both liquid side

volumetric mass transfer coefficient and interfacial area are increased by an

increase of the superficial gas velocity, while at a fixed superficial gas

velocity when increasing the superficial velocity only the liquid side

volumetric mass transfer coefficient is increased. This is because in the

former case, the bubble length increases resulting to an increase of the gas-

liquid interfacial area, while in the latter case it is the liquid film around the


Page 47

gas bubbles that becomes thicker in which case the interfacial area remains

approximately the same.

Sobieszuk et al. [107] studied CO2 absorption into a K2CO3/KHCO3 aqueous

buffer solution containing hypochlorite catalyst in a circular capillary of

0.4mm diameter and measured the mass transfer characteristics of that

system. They also compared their measured mass transfer coefficients with

the corresponding literature correlations (2.6), (2.7) and (2.11). They

concluded that the correlation from Yue et al. (2.11) is very close to their

results, while the correlations of Bercic and Pintar (2.6) and of Vandu (2.7)

overestimated their results.

2.3.3 Void Fraction in Gas-Liquid Systems

Void fraction of a multiphase system in a microchannel is the fraction of

volume the gas occupies to the total volume of the channel as shown in

(2.12),

휀𝑔 =

𝑉𝑔

𝑉𝑡𝑜𝑡𝑎𝑙= 1 −

𝜏ℓ∙𝜐ℓ

𝑉𝑡𝑜𝑡𝑎𝑙 (2.12)

where is the liquid mean residence time [s], 𝑉𝑡𝑜𝑡𝑎𝑙 is the volume of the

reactor [m3] and 𝜐ℓ is the volumetric flow rate of liquid [m3/s].

When studying a multiphase reaction in a microchannel, knowledge of the

void fraction of the system is essential for the determination of the reaction

volume, the pressure drop along a channel and the mass and heat transfer

characteristics which is crucial for the design of microstructured process

devices for gas-liquid or gas-liquid solid systems such as multiphase

reactors.

There are several models available in the literature for the calculation of void

fraction of as gas-liquid system in microchannels. These models are

summarised in Table 2-3 together with the experimental conditions for

which these are valid.


Page 48

Table 2-3 Void fraction correlations for gas-liquid systems.

C: circular, R: rectangular, : volumetric quality.

One of the simplest and most commonly used correlations for the calculation

of the void fraction of a multiphase system in capillaries is the homogenous

model (2.13) which is based on the assumption that there is no slip between

the gas-liquid two phases.

(2.13)

where 𝛽 is the volumetric quality of the system defined as 𝑗𝑔 (𝑗𝑔 + 𝑗ℓ)⁄ .

This assumption is valid mainly for homogeneous flows. Bubbly flow is a

typical example of a homogeneous flow, as discrete gas bubbles are

entrained in a continuous liquid phase. On the other hand, this correlation

cannon be applied with confidence in non-homogeneous flows such as slug,

churn and annular flows, where bubbles rise with higher velocities than the

liquid phase.

g

g

g

j

j j

Author/source Correlation Experimental

condition

Homogeneous -

Armand [108]

휀𝑔 = 0.833 ∙ 𝛽

Triplett et. al. [76]

휀𝑔 = (0.28 ∙ (1 − 𝛽

𝛽)

0.64

∙ (𝜌𝑔

𝜌ℓ)

0.36

∙ (𝜇𝑔

𝜇ℓ)

0.07

+ 1)

−1

Air-water ID=1.1, 1.45mm (C) ID=1.09, 1.49mm (R) jG= 0.022-80 m/s jL= 0.02-8 m/s

Serizawa et al. [71]

휀𝑔 = 0.69 ∙ 𝛽 + 0.0858

Air-water ID= 0.02-0.1 mm (C) jG= 0.0012-295.3 m/s jL= 0.003-17.52 m/s

Kawahara et al. [78]

휀𝑔 =0.69 ∙ 𝛽0.5

1 − 0.97 ∙ 𝛽0.5

N2- water ID=0.1 mm (C) jG = 0.1-60 m/s jL = 0.02-4 m/s

Saisorn et al. [109]

휀𝑔 =0.036 ∙ 𝛽0.5

1 − 0.945 ∙ 𝛽0.5

Air-water ID=0.15 mm (R)

g

g

g

j

j j

0.9


Page 49

Indeed, when Triplett et al. [76] measured the void fraction of and air/water

system in circular and rectangular microchannels for bubbly, slug and

annular flow, found that the homogenous model predicted satisfactory their

data only in the case of bubbly and slug flow, while overpredicted them in

the case of annular flow. For this reason, they developed a correlation (2.14)

that can describe the full set of their data for bubbly, slug and annular flow

in circular and rectangular microchannels.

휀𝑔 = (0.28 ∙ (

1 − 𝛽

𝛽)

0.64

∙ (𝜌𝑔

𝜌ℓ)

0.36

∙ (𝜇𝑔

𝜇ℓ)

0.07

+ 1)

−1

(2.14)

In order to take into account the slip effect, other researchers [71,78,108]

introduced a prefactor A in the homogeneous model (2.13) to develop void

fraction correlations that can describe their data, as shown in (2.15),

휀𝑔 = 𝐴

𝑗𝑔

𝑗𝑔 + 𝑗ℓ= 𝐴 ∙ 𝛽 (2.15)

where A is an empirical numerical prefactor that can be estimated based on

experimental observations that ranges between 0 and 1. All of these models

show linear relationship between the void fraction and the volumetric

quality and are valid for microchannels with inner diameters larger than

250µm. One of the most commonly used models for void fraction prediction

is that of Armand [108] in which A=0.833.

There are several studies in the literature [71,72,110] where researchers have

measured the void fraction of gas-liquid systems in microchannels by means

of flow observation and have confirmed that Armand’s correlation is in good

agreement with their experimental data for slug flow.

On the contrary, the relationship between the void fraction and the flow

quality β seems to become non-linear for very small microchannels

(ID<250μm) [72,78,109].


Page 50

Chung and Kawaji [72] studied the effect of the channel diameter on the two-

phase flow of a nitrogen-water system in circular capillaries and observed

this non-linear relationship between the void fraction and the flow quality in

small capillaries (ID<250μm).

2.3.4 Experimental Techniques for Void Fraction and Residence Time

Distribution Studies

Various methods have been demonstrated in literature to measure

experimentally the void fraction and other flow characteristics of gas-liquid

systems in microchannels. The most common techniques researchers used in

the past are flow observation [70-72,78], other optical techniques [111],

residence time distribution experiments and electrical impedance [112]. All

these techniques, their benefits and applications are discussed below.

2.3.5.1 Flow Observation

The most common technique to estimate the void fraction of a gas-liquid

system is by analysing pictures of the two-phase flow recorded in the

microchannel [70-72,78]. The benefit of this method is its simplicity as its

main requirement is a good quality high speed camera or microscope to

produce high quality images in the smooth and well-define interface

configuration microchannels provide. The instantaneous void fraction is

computed as the ratio of the gas volume to the total channel volume within

the viewing window. For example, the images are assigned a void fraction of

zero when they show only the liquid flowing alone in the entire view

window or a void fraction of unity when they show a continuous gas core

with a ring-shaped liquid film. The time-averaged void fraction is then

obtained by averaging the instantaneous void fraction values from the total

amount of images taken [70]. The drawback of this technique is that images

of fast moving gas plugs are blurred at the nose and tail, which results in

uncertainty when analysing the images and defining the sizes of the gas

plugs. Furthermore, this technique requires a transparent microchannel to


Page 51

allow the observation of the flow, which is not always feasible (e.g at high

pressure systems metal channels are commonly used). Finally, this technique

cannot be applied in conditions in which intermittent phenomena occur.

2.3.5.2 Other Optical Techniques

Ide et al. [111] used multiple optical fiber probes to measure the gas plug

size, velocity and void fraction for a water/nitrogen system in 100μm

circular microchannels. Based on the electrical signals from photodiodes the

presence of gas or liquid phase was identified at the measurement location in

the microchannel. In addition, the use of multiple fiber probes installed in

different points across the microchannel allowed the determination of the

speed and consequently the length of gas bubbles and liquid plugs. This

technique offers great accuracy on the measurements of flow characteristics

compared to flow observation where the shutter speed of the imaging

equipment must be very high to capture sharp images of the two-phase flow.

Paranjape et al. [112] used electrical impedance to measure the void fraction

of an air/water system in microchannels with a hydraulic diameter of

780μm. The practical implementation of the electronic circuit measures the

net electrical admittance (i.e. the inverse of the electrical impedance), which

is a function of the void fraction and the flow pattern of the system when it is

appropriately normalised for a given geometry of electrodes.

2.3.5.3 Residence time distribution

Another non-intrusive void fraction measurement technique is based on

residence time distribution experiments (RTD). For a single-phase flow

system, the mean residence time is defined as,

𝜏 =

𝑉𝑟

υ (2.16)

where 𝑉𝑟 is the volume of the channel and υ is the volumetric flow rate of the

fluid.


Page 52

When considering a gas-liquid system, the mean residence time of the liquid

is calculated based on (2.17).

𝜏 = (1 − 휀𝑔)

𝑉𝑟

υℓ (2.17)

where υℓ is the liquid volumetric flowrate and 휀𝑔 is the gas void fraction of

the system. Hence, by performing RTD experiments and measuring the

liquid mean residence time of the system one can then determine the void

fraction of the system.

Danckwerts [113] first presented a methodology to study the RTD of a fluid

by a step or a pulse change in one of the properties of the fluid (e.g. colour,

concentration) in the inlet of the channel and monitoring then this change in

the outlet. Consider a fluid flowing at a volumetric flowrate through a vessel

of volume V. At time t=0 the main fluid is switched to a tracer of

concentration Cmax (step-input change). The transition of the measured

concentration, Cstep, against time is shown in Figure 2.6 [8]. The

dimensionless form of the Cstep curve is called the F curve.

Figure 2.6 Residence time distribution experiment based on an step-input change [8].

The mean residence time of the fluid is then calculated based on (2.18),

𝜏 =∫ 𝑡 𝑑𝐶𝑠𝑡𝑒𝑝

𝐶𝑚𝑎𝑥

0

∫ 𝑑𝐶𝑠𝑡𝑒𝑝𝐶𝑚𝑎𝑥

0

=1

𝐶𝑚𝑎𝑥∫ 𝑡 𝑑𝐶𝑠𝑡𝑒𝑝

𝐶𝑚𝑎𝑥

0

(2.18)


Page 53

In cases where the tracer input deviates largely from the assumption of a

perfectly sharp step (for a step-input experiment), the fact that the

concentration of the tracer in the inlet is a function of time should be taken

into account. The concentration of the tracer in the outlet needs to be

modified in order to take into account this deviation from the perfect tracer

input by the convolution integral [8]. This type of problem is often faced

during experimentation and while is quite straightforward to convolute, it is

quite hard to deconvolute and requires extensive modelling.

Apart from the mean residence time and residence time distribution of a

system, information about dispersion along the reactor can be obtained from

RTD experiments. When considering a fluid that flows through a vessel in a

continuous process, the most common assumption that is taken for

simplification of the problem is either that the fluid is completely mixed in

the vessel or that there is plug flow behaviour [113]. The mixing quality of

the system can be studied by analysing how much the shape of the

concentration curve changes between the inlet and the outlet- the steeper the

curve in the outlet the more plug-flow behaviour the system presents.

More specifically, for a flow system that behaves like an open vessel the

characterization of the spread of the tracer along the channel can be studied

by analysing the dispersion number, 𝐷

𝑢𝐿, where D is the dispersion coefficient.

A large dispersion coefficient number shows fast tracer spread in the fluid,

while a zero value indicates plug-flow behaviour.

Experimentally the dispersion number can be determined by the shape of the

E curve (Figure 2.7) and (2.19),

𝜎𝜃

2 = 2𝐷

𝑢𝐿

(2.19)

where 𝜎𝜃2is the variance which can be determined from the tracer response

curve and θ is the dimensionless time (θ=t/τ). It should be noted that (2.19)


Page 54

can only be used for systems with small range of dispersion (𝐷

𝑢𝐿< 0.01). For

systems with large range of dispersion (𝐷

𝑢𝐿> 0.01) (2.20) should be used.

𝜎𝜃2 = 8 (

𝐷

𝑢𝐿)

2

+ 2𝐷

𝑢𝐿

(2.20)

Figure 2.7 Typical tracer response curve for ‘open vessels’ and relationship with the

dispersion number, 𝑫

𝒖𝑳 [8].

In order this analysis to be valid one should ensure that the system is in the

dispersion and not the convection region based on Figure 4.5.

The criterion to evaluate how much a flow deviates from plug flow

behaviour is based on the vessel dispersion number, D uL [8]. If 0.01D uL ,

the deviation from plug flow is small while if 0.01D uL , the flow deviates

largely from plug flow.

RTD experiments have been widely used in the literature to characterize

hydrodynamic characteristics in microchannels such as the residence time,

the void fraction and the axial dispersion in a single phase and multiphase

systems in microreactors. Many researchers [114-119] have evaluated the

performance of microreactors with different designs by studying the RTD of

of the system using different techniques of injecting the tracer. Gunther et al.


Page 55

[120] measured the RTD in test tube reactors and a micromixer using a pulse

marking with a dye tracer and applying the axial dispersion model and the

tracer was detected by analysing the transmittance by a self-developed

transmittance sensor. Lohse et al. [121] developed a RTD measurement

technique for microreactors based on a tracer ‘injection’ using the optical

activation of a caged fluorescent dye creating this way ideal signals at

arbitrary positions even in complex-structured microreactors. Trachsel et al.

[116] presented a piezoelectrically activated tracer injection technique that

produces almost perfect pulse signals. The distribution of the tracer was

monitored with fluorescence microscopy. Cantu-Perez et al.[114] studied

numerically and experimentally the RTD in rectangular channels with and

without herringbone structures. For the numerical study particle tracking

with random walk diffusion was used while for the experimental study the

concentration of the tracer dye was monitored by a LED-photodiode system.

Only a few studies however are available in the literature for RTD

measurements of gas-liquid systems under reaction conditions. Zhang et al.

[118] studied recently the RTD of gas-liquid systems (cyclohexane or

toluene-nitrogen) in minichannels (Stainless Steel tubing with ID=2mm and

L=32.45m) under reaction conditions (165oC, 1MPa) under slug and under

annular flow. The RTD of the liquid phase was determined using the pulsing

tracer method and the tracer concentration was measured in the exit using

gas chromatography. They found that the RTD of the liquid phase under

high temperature was different than that at room temperature due to the

evaporation and condensation of the liquid inside the channel. They also

observed that their RTD curves became wider by increasing the gas flowrate

or by decreasing the liquid flowrate. This was due to the backmixing of the

liquid phase at higher gas flowrates resulting in a significant dispersion of

the tracer.


Page 56

2.4 Homogeneous Catalysis: Methoxycarbonylation of

Ethylene

Catalysis plays a crucial role in today’s chemical industry as more than 85%

of its products made in catalytic processes. Catalysts are widely used for the

production of fuels, bulk and fine chemicals and polymers and are

indispensable in preventing pollution by avoiding formation of unwanted

products and hence waste. A catalyst accelerates a chemical reaction by

offering an alternate mechanism for the reactants to become products with

lower activation energy.

Homogeneous catalysis is a sequence of reactions that involve a catalyst in

the same phase as the reactants, usually in liquid phase. During the last

decades many homogenous catalytic processes use organometallic

complexes as catalysts. Organometallic catalysts consist of a central metal

surrounded by organic and inorganic ligands and their success is based on

the easy modification of their environment by ligand exchange. Once the

ligands are coordinated the reactivity of the metals may change significantly.

Palladium is one of the most widely used metals in organometallic chemistry

as due to its versatility, catalyses a large number of organic reactions such as

polymerization of alkenes, carbonylation of alkenes, Heck reaction, Suzuki

reaction, alkylic alkylation, etc. [122].

2.5.1 Carbonylation reactions in microreactors

Carbonylation reactions are homogeneously catalysed reactions that involve

the introduction of C=O into an organic molecule such as alkenes, alkynes,

or dienes. The nucleophile can be water, alcohol or acid and the products are

acids, esters or anhydrides. Traditionally, these reactions have been carried

out glass batch flasks or stainless steel autoclave reactors. However, the

rapid development of microreactor technology over the past two decades has

brought significant benefits to chemical synthesis over batch reactors, such as

large surface to volume ratio, high heat and mass transfer rates and high


Page 57

operational safety. Specifically for the carbonylation reactions, the small

reaction volumes in microreactors allow the use of high CO pressure with

great safety compared to batch reaction systems. Moreover, due to the

efficient mixing, the environmental impact is also improved as significant

smaller amounts of carbon monoxide (and other toxic substances) are

required. On the contrary in autoclave reactors, two third of the vessel

typically needs to be filled with waste CO. Nowadays, a wide range of

carbonylation reaction has been demonstrated in microstructured reactors.

Long et al. [123] studied the palladium catalysed carbonylation of

iodobenzene in a microchannel and reported higher yield of the

aminocarbonylation product compared to batch operation even with a

longer reaction time.

Murphy et al. [44] constructed microreactors capable of reaching pressures

exceeding 100bar and demonstrated its advantages on Heck carbonylation

reactions. They studied the palladium catalysed carbonylation of p-

iodocyanobenzene and reported the ease in handling toxic or air sensitive

compounds such as carbon monoxide and palladium as another advantage

of closed and small reaction volume systems.

Fukuyama and co-workers studied radical [124], metal-catalysed

carbonylation [123,125] and radical-based carbonylation reactions [126] using

microstructured devices and highlighted the precise control of reaction

temperature and residence time compared to batch systems that lead in

greater reaction yields and operation safety. They also demonstrated the

mixing efficiency due to the gas-liquid segmented flow that resulted to large

gas-liquid interphase and facilitated carbon monoxide diffusion in the liquid

slugs, leading to much lower CO pressures required in the system for the

satisfactory yields [125].

Takebayashi et al. [127] demonstrated also the importance of the segmented

flow in the reductive carbonylation of nitrobenzene. They reported higher


Page 58

yields of phenylisocyanate when the reactions were carried out in smaller

inner diameter tubing (0.5mm instead of 1mm), attributed to the shorter

liquid slugs resulting in larger interfacial area.

Keybl et al. [47] demonstrated a microreactor system for the study of

homogenous catalysis at high temperature and pressure conditions (<350oC

and 100bar) under continuous flow by studying the hydroformylation of 1-

octene. They reported that segmented gas-liquid flow reduced the axial

dispersion and isothermal operation was easily established. The only benefit

of batch reactors they reported compared to flow reactors was that the

efficiency and ease of the former when collecting time series data.

Miller et al. [128,129] developed a glass microfabricated device for rapid

catalyst screening of the aminocarbonylation of iodobenzene in a range of

temperatures (75-150oC). They highlighted that for the catalyst screening in

microreactors only small quantities of catalyst and reagents were needed

compared to batch systems.

2.5.2 Methoxycarbonylation of ethylene

Methoxycarbonylation of ethylene is a homogeneous palladium catalysed

reaction for the production of methyl propionate (2.21), an intermediate for

the production of methyl methacrylate.

𝐶2𝐻4 + 𝐶𝑂 + 𝐶𝐻3𝑂𝐻 → 𝐶2𝐻5𝐶𝑂𝑂𝐶𝐻3 (2.21)

The reaction between carbon monoxide, ethylene and methanol can also give

rise to other products such as polyketones, materials with very high

mechanical strength and flexibility. A possible route for the production of

polyketones or methyl propionate is the use of palladium catalysts as

discovered by Gouch et al [130]. However, very harsh conditions are

required and the process only produced very small amounts of products. Sen

et al. [131] observed that use of palladium together with weakly coordinated

anion, phosphine and ligands results to more stable and active catalyst


Page 59

complexes for the formation of polyketones from carbon monoxide, ethylene

in alcohol solvents under milder conditions. Drent et al. [132] discovered that

cationic palladium complexes containing tertiary phosphines and weakly

coordinated anions in methanol are very efficient for producing methyl

propionate from carbon monoxide and ethylene. However, when using

catalysts containing bidentate tertiary phosphine ligands no methyl

propionate is formed but only high molecular weight polyketones [133].

Hence, it was concluded that monodentate phosphines are the most suitable

for the production of methyl priopionate. However, later several bidentate

ligands were found to be highly selective for the production of methyl

propionate with high reaction rates [134]. It is hence clear that the ligand’s

choice is very important as different ligands can result to significantly

different products. It was concluded that the most suitable ligand for the

production of methyl propionate is the 1,2-bis[(di-tert-

butylphosphino)methyl]benzene or dtbpx.

Another factor that was found to affect largely both the reaction rate and the

molecular weight of the product (polyketones) is the amount and the nature

of the acid whose main role in these catalysts is to introduce the anion. It was

observed that the reaction rate increased significantly when using weakly

coordinating anions as they favour coordination of the monomer [135].

Considering the effect of the acid amount added it was found that significant

excess of acid leads to higher reaction rates [135]. However, at high acid

concentrations the acid found to act as a poison and the anion found to start

competing with the monomers for the coordination sites of the metal.

In the Lucite process, the catalyst is formed in situ via the reaction of

[Pd(dtbpx)(dba)] (dba = trans,trans-(PhCH=CH)2CO] with CH3SO3H in

MeOH. The catalyst is capable of converting ethylene, carbon monoxide and

methanol to methyl propionate at a rate of 50,000 mol of product per mol of

catalyst per hour with a selectivity of 99.98% under very mild conditions


Page 60

(80oC, 10atm of C2H4/CO)[1,132]. The large selectivity and yield at such

mild conditions make this process very attractive industrially.

Different catalysts based on [Pt(dtbpx)(dba)] and RSO3H (R = CF3, CH3) have

been studied for the production of methyl propionate but they were found

much less active than the palladium analogue [136]. Other bidentate ligands

have been also investigated for the same process, but it was found that dtbpx

gave the best results [137].

2.5.3 Proposed Mechanisms for Polyketones/Methyl Propionate

Formation

There are two mechanistic pathways proposed to describe the mechanism of

palladium catalysed methoxycarbonylation of ethylene [134] for the

production of both methyl propionate and polyketones as shown in Figure

2.8. Methyl propionate formation and polyketone formation share the

initiation and termination steps, however for the former termination occurs

after a single turnover [138]. This suggests that only one cycle; either hydride

or methoxy is operative in the formation of methyl propionate.

Figure 2.8 Proposed mechanisms for the formation of polyketones and methyl propionate.


Page 61

The methoxy cycle (B) starts with insertion of carbon monoxide in the

palladium methoxy bond. Then, ethylene is added in the Pd-carbon bond of

the alkoxycarbonyl-palladium complex. The final step is the addition of

methanol that produces methyl propionate and generates the initial alkoxy

palladium complex.

The hydride cycle (A) starts with insertion of ethylene in the palladium

hydride bond forming an alkyl complex. Then, insertion of carbon monoxide

is followed to produce an acyl complex. Last step is addition of methanol

that produces methyl propionate and regenerates the palladium hydride.

Extensive studies of Clegg et al. [139] have shown that the

methoxycarbonylation of ethylene using Alpha process follows a hydride

catalytic cycle based on characterisation of all the intermediates which was

also confirmed with another study based on isotope scrambling experiments

[140].

Page 62

CHAPTER 3. Reactor Model Development and

Validation

3.1 Introduction

Reactor model is a mathematical model that is able to describe the

phenomena happening in a reactor. It is an essential tool in chemical reactor

engineering and is used widely for the design of new reactors but also for the

kinetic study of reaction systems. There are reactor models available in the

literature for some main reactor designs such as the ideal plug flow and

continuously stirred reactors. However, for reactors deviating from this

ideal-behaviour, one should develop a customised reactor model for the

specific reaction system. Then, the validity of the developed reactor model

should be confirmed with experimental data of a model system, a system

with known kinetics. In our case, a simplified one-dimensional plug flow

reactor model was developed in order to be then used for the kinetic study of

an homogenous catalysed gas-liquid system, the methoxycarbonylation of

ethylene (Chapter 5-Chapter 6). The reactor model was first validated with

experiments with a model reaction system, the carbon dioxide absorption in

buffer solutions, a well-studied reaction system with simple kinetics in order

to ensure its validity to describe gas-liquid reaction systems in capillary

reactors.

3.2 Reaction System

The validity and suitability of a reactor model should be demonstrated by

choosing a well-studied reaction system with kinetics that has been

previously described in detail. An ideal model reaction system has simple

kinetics and its main characteristics are similar to the main reaction system

one wants to study. In our case, the main goal is the kinetic study of the

methoxycarbonylation of ethylene, hence it is essential to ensure that there

are no mass transfer resistances and therefore the experimental results are

CHAPTER 3. Reactor Model Development and Validation

Page 63

intrinsic data. Therefore, the model reaction should operate in the slow

regime in order to fulfil this criterion. A suitable model reaction for our

system is the absorption of carbon dioxide in buffer solutions.

Carbon dioxide in alkaline solutions is a reaction system that has been

studied to a large extent by several authors [5,141-152] in the past and the

kinetics of this reaction system has been described in detail.

When CO2 is absorbed by a HCO3-/CO32- solution, two reactions may occur,

𝐶𝑂2 + 𝑂𝐻−𝑘1→ 𝐻𝐶𝑂3

− (3.1)

𝐶𝑂2 + 𝐻2𝑂𝑘2→ 𝐻𝐶𝑂3

− + 𝐻+ (3.2)

According to Nysing et al [141], the reaction (3.1) predominates over the

reaction (3.2), which is of comparable importance only when pH<8. In

addition, reaction (3.1) can be considered reversible only when pH>10. Both

reactions are accompanied by the following instantaneous reactions,

𝐶𝑂32− + 𝐻+ → 𝐻𝐶𝑂3

− (3.3)

𝐶𝑂32− + 𝐻2𝑂

𝐾4↔ 𝐻𝐶𝑂3

− + 𝑂𝐻− (3.4)

The overall reaction is,

𝐶𝑂2 + 𝐶𝑂32− + 𝐻2𝑂 → 2𝐻𝐶𝑂3

− (3.5)

Astarita [5] showed that the kinetics of reaction (3.5) can be expressed by,

𝑟 = (𝑘2 + 𝑘1 ∙ 𝐶𝑂𝐻−) ∙ 𝐶𝐶𝑂2 (3.6)

where the concentration 𝐶𝑂𝐻− in the buffer solution is derived by the

equilibrium reaction (3.4),

𝐶𝑂𝐻− = 𝐾4 ∙

𝐶𝐶𝑂32−

𝐶𝐻𝐶𝑂3−

= 𝐾4 ∙ 𝛽𝑐 (3.7)

and where 𝛽𝑐 is the carbonate-to-bicarbonate ratio, 𝐶

𝐶𝑂32−

𝐶𝐻𝐶𝑂3−.


Page 64

In addition, Astarita [5] reported that for any solution which is not

completely converted to bicarbonate, k2 may be neglected. Consequently, the

reaction may be considered as a pseudo first order with kinetic equation,

𝑟 = 𝑘 ∙ 𝐶𝑂2 (3.8)

where,

𝑘 = 𝑘1 ∙ 𝐾4 ∙ 𝛽𝑐 (3.9)

Pinsent et al [142] reported that the activation energy of k1 is 13,250 cal while

Nysing et al [141] measured the product 1 4k K in different temperatures and

in different concentrations of sodium and potassium bicarbonate in a wetted

wall column, where it appears that the value of k for potassium buffer

solutions is higher than for sodium buffer solutions. The assumptions that

they made were that the reaction product is not volatile, the diffusivity is

constant, there is no heat effect and the concentration of hydroxide ions is

constant. In addition, Nysing et al [141] reported that in order to keep the

concentration of hydroxide ions constant, there should be small partial

pressure of CO2, small contact time of CO2, low temperature, high carbonate

concentration and low ratio of carbonate and bicarbonate concentrations. It

should be noted that, from their results, it appears that the bicarbonate

concentration does not affect significantly the value of k but it affects the

solubility of CO2.

Furthermore, Astarita [5] concluded that at low carbonate-to-bicarbonate

concentrations the reaction takes place in the slow reaction regime when

studying this reaction system in a packed tower.

3.2.1 Operating Conditions of Reaction System

As it was mentioned earlier, the main criterion that the reaction should fulfil

in order to be suitable for a kinetic study is to take place in the slow regime.


Page 65

Danckwerts [7], using some past experimental data of carbon dioxide

absorption in carbonate/bicarbonate solutions in a bubble plate, showed that

the reaction in the film is negligible and therefore the reaction is slow,

calculating the Hatta number for a first order reaction. He concluded that the

criterion below is a necessary condition to ensure that the reaction takes

place only in the liquid bulk.

𝐻𝑎 =


𝑘ℓ< 0.3 (3.10)

In order to identify the optimum conditions under which the reaction system

would be the slowest possible, the reaction rate constant was calculated in

different temperature conditions and under various ratios of carbonate to

bicarbonate concentrations by means of (3.9). Values of the product 1 4k K at

different temperatures were given by Nysing et al. [141]. The results are

presented in Table 3-1. The diffusion coefficient of carbon dioxide in

carbonate/bicarbonate buffer solutions was measured by R. Zeebe [153] and

found equal to 14∙10-9 m2/s. The liquid side mass transfer coefficient, kL, for

carbon dioxide in carbonate/bicarbonate buffer solutions in microchannels

was reported by Yue et al. [99] equal to 8∙10-4 m/s.

Table 3-1 Reaction rate constant k (s-1) under different temperature conditions, T (oC), and ratios of carbonate to bicarbonate concentrations, βc.

T(oC) k1K4(s-1) βc k(s-1)

10

0.21

1/9 0.0238

1 0.21

9 1.89

20

0.56

1/9 0.062

1 0.56

9 5.04

30

1.4

1/9 0.16

1 1.4

9 12.6


Page 66

It is clear that when decreasing the temperature the reaction rate constant

decreases, resulting to a slower reaction performance. The ratio of carbonate

to bicarbonate appears to have similarly a negative effect. Hence, it can be

concluded that the optimum conditions in order to operate in the slow

regime are low temperature conditions and low ratio of carbonate to

bicarbonate concentrations at atmospheric pressure.

3.2.2 Effect of Reaction Extent on Reaction Rate Constant

As it was described earlier, the reaction rate constant at 10oC and at 20oC is

given by (3.11) and (3.12) respectively,

𝑘𝑟 = 0.21 ∙ 𝛽𝑐 𝑎𝑡 10 𝐶𝑜 (3.11)

𝑘𝑟 = 0.56 ∙ 𝛽𝑐 𝑎𝑡 20 𝐶𝑜 (3.12)

where c is the ratio of the carbonate over the bicarbonate concentration.

However, along the capillary reactor, as the reaction takes place, carbonate

species are being consumed while bicarbonate species are being produced as

the stoichiometry of the reaction shows in Table 3-2, where, is the molar

flowrate of the carbon dioxide in the gas phase in the inlet of the reactor,

is the inlet flowrate of the carbonate, the inlet flowrate of the

bicarbonate and the conversion of CO2 that is defined by (3.13),

𝑋𝐶𝑂2

= 1 −𝐹𝐶𝑂2,ℓ + 𝐹𝐶𝑂2,𝑔

𝐹𝐶𝑂2,𝑔𝑜 (3.13)

where is the molar flowrate of the carbon dioxide in the gas phase in

the inlet of the reactor.

Table 3-2 Stoichiometric table of the reaction in the capillary reactor.

𝑪𝑶𝟐 + 𝑪𝑶𝟑𝟐− + H2O → 𝟐𝑯𝑪𝑶𝟑

−

Inlet 2

0

COF 2

3

0

COF

3

0

HCOF

Reacted 22

0

COCOF X

22

0

COCOF X

22

02 COCOF X

Outlet 22

0 (1 )COCOF X 2

23 2

0 0

COCO COF F X

23 2

0 02 COHCO COF F X

2

0

COF

23

0

COF

3

0

HCOF

2COX

2

0

,CO gF


Page 67

The ratio, 𝛽𝑐 , is expressed as a function of the conversion of the reacted

carbon dioxide by (3.14),

𝛽𝑐 =𝐶𝐶𝑂3

2−

𝐶𝐻𝐶𝑂3−

=

𝐹𝐶𝑂32−

𝜐ℓ

𝐹𝐻𝐶𝑂3−

𝜐ℓ

=𝐹𝐶𝑂3

2−


=𝐹𝐶𝑂3

2−0 − 𝐹

𝐶𝑂2

0,ℓ 𝑋𝐶𝑂2


0 + 2𝐹𝐶𝑂2

0,ℓ 𝑋𝐶𝑂2

(3.14)

Considering a gas-liquid stream of 0.1ml/min 20% CO2 and 0.02ml/min

Na2CO3:NaHCO3 (1:9) flowing together through a capillary reactor of 0.5mm

inner diameter at 10oC, the ratio, 𝛽𝑐, and the reaction rate of the system is

plotted against carbon dioxide conversion based on equations (3.11), (3.14)

and (3.13). Due to the excess of carbon dioxide, the assumption that there is

always equilibrium in the gas-liquid interphase and the slow nature of this

reaction, it was assumed that the liquid phase is always saturated to carbon

dioxide. The results are shown in Figure 3.1 and Figure 3.2, where it is

shown that the change of the carbonate-to-bicarbonate ratio, 𝛽𝑐 , against

carbon dioxide conversion is significant due to the reaction that leads to

consumption of carbonate species and production of bicarbonate species.

Figure 3.1 Effect of reaction extent on carbonate: bicarbonate ratio, 𝜷𝒄, along a capillary reactor (L=1m, ID=0.5mm) for an initial 0.1M sodium carbonate:

bicarbonate (1:9) solution.


Page 68

Moreover, the decrease of the ratio, 𝛽𝑐 , as the reaction proceeds has a

consequent effect on the reaction rate expression as expected by (3.11). This

is also demonstrated in Figure 3.2, where the reaction rate decreases as a

function of carbon dioxide conversion. In addition, it is noteworthy that

while the reaction proceeds it becomes slower because of the decrease on the

ratio, 𝛽𝑐.

Figure 3.2 Effect of reaction extent on reaction rate constant, kr, along a capillary reactor (L=1m, ID=0.5mm) when kr,0=0.0233 (T=10oC and βc=0.111).

It can be concluded that the reaction rate constant expression does not

remain constant but is a function of carbon dioxide conversion. Hence, all the

relevant equations should be included in the reactor model for an accurate

simulation of this reaction system.

3.2.3 Effect of Reaction Extent on Solubility of Carbon Dioxide

Solubility of carbon dioxide is a very important parameter as it defines the

amount of carbon dioxide that will be dissolved in the liquid phase and

hence it will be available for reaction. There are correlations available in the

literature [7] that calculate the solubility of various gases in electrolyte

solutions such as this system. In general, the solubility of a gas in an


Page 69

electrolyte solution is affected largely by the temperature as well as the ionic

strength of the solution. Schumpe [154] proposed a correlation to describe

the effect of dissolved salts on the solubility of a gas.

0log i g i

i

Hh h C

H

(3.15)

where 0H

H is the ratio of the gas solubility in water to that in a salt solution,

ih , gh are referred in the literature as Sechenov constants and iC is the

concentration of the ion in the solution. The parameters ih which are specific

to each ion present in the solution and the parameter gh which is

characteristic to the absorbed gas (CO2) in the solution are available in the

literature [154] at 298K and are given in Table 3-3.

However, according to Schumpe [154] due to the weak effect of the

temperature on the Sechenov constants, these values can be applied in a

wider temperature range with confidence, by using the gas solubility in

water at the respective temperature. For higher accuracy, Schumpe et al [155]

proposed also a correlation to describe the temperature effect on the

Sechenov constants and concluded that there is an approximately linear

decrease of them with temperature. Furthermore, the solubility of CO2 in

water is available in a wide temperature range in the literature [156] and it

was found equal with 30.053kmol m atm at 283K.

Table 3-3 Values of Sechenov constants ih and gh at 298K [154].

ion hi (m3/kmol) gas hg (m3/kmol)

Na+ 0,1171 CO2 -0,0183

HCO3- 0,1372

CO32- 0,1666

Consequently, in the present work the calculated by (3.15) value of the

equilibrium solubility of carbon dioxide in a sodium carbonate/bicarbonate


Page 70

buffer solution at 283K and at 293K is 0.05mol Latm and 0.037mol Latm

respectively. These values are correct when assuming that the ratio of

carbonate-bicarbonate remain constant along the reactor. However, it was

shown earlier that in reality this ratio is changing along the reactor, as the

reaction proceeds and carbon dioxide conversion increases, due to the

reaction between carbon dioxide and carbonate species. The effect of the

reaction extent on the solubility of carbon dioxide due to the ratio change is

studied in Figure 3.3, where its solubility is plotted against carbon dioxide

conversion.

Figure 3.3 Effect of carbon dioxide conversion on carbon dioxide solubility in a

carbonate-bicarbonate solution in a capillary reactor at 10oC.

In Figure 3.3, it is shown that even for a 40% conversion, the solubility

change is insignificant (<0.6%). Hence, it can be concluded that the change of

carbon dioxide solubility along the reactor is insignificant and therefore it

can be considered constant along the reactor.

3.3 Experimental Set-Up: Reaction and Analysis System

The schematic diagram of the experimental set-up used for the study of the

model system is shown in Figure 3.4. A syringe pump (kdScientific) is used


Page 71

to deliver the liquid fluid (sodium carbonate: bicarbonate buffer solution,

1:9), through a pulse dampener, then a liquid filter (for particles above 10μm)

to the tee-junction where it meets the gas mixture (2% CO2, 98% N2). This T-

junction has a low swept volume of 2.9μL with thru-hole of 0.5mm. The first

gas stream is a 20 vol% CO2, 80 vol% N2 mixture and its flowrate is

controlled by a mass flow controller (Bronkhorst LTD, 0-1ml/min). Then, it

is mixed with a second gas stream (N2), which is controlled by another mass

flow controller (Brooks 5850, 0-3ml/min) and dilutes the 20% CO2 mixture to

a 2% CO2 mixture. The gas mixture (2% CO2/N2) passes through a non-

return valve, a pressure relief valve (up to 17bar) and then mixes with the

liquid. Following this, the gas-liquid mixture passes through the capillary

microreactor.

Figure 3.4 Schematic diagram of the experimental set-up for the study of the carbon

dioxide absorption in a carbonate-bicarbonate buffer solution.

Two capillary reactors made of glass were used with 1m length and internal

diameter 1mm and 0.5mm respectively. After the microreactor, the gas-

liquid mixture enters a glass microseparator (Figure 3.5) from which the

liquid is being collected in a flask while the gas is being analysed online by

the GC. More photos of the experimental set-up can be found in the

Appendix B.


Page 72

Experiments with the model reaction were conducted at two different

temperature conditions (20oC and 10oC). A water bath (Polystat cc2) was

used to cool the microreactor down to 10oC and control the temperature.

Leak test was conducted by pressuring the system and no leaks were found.

In the beginning of every run, the microseparator was primed with the

liquid solution. Generally, the glass separator was separating effectively the

gas-liquid stream. Rarely some bubbles were going to the liquid phase but

this was not crucial because the goal was to prevent liquid flow to the gas

exit as after the separator the gas was being analyzed online with GC

analysis. To ensure that no liquid flows into the GC, a liquid trap with small

volume was placed after the gas exit of the separator.

Figure 3.5 Picture of the glass reactor (L=1m, ID=1mm) and the glass microseparator where gas is being separated from the liquid and is analysed by GC.

The two mass flow controllers (MFC) were calibrated using a bubble meter

at NTP conditions (20oC, 1bar). The calibration results were also corrected for

the moisture effect and the temperature effect based on (3.16).

exp cal s

real

cal cal

T P PVF

t T P

(3.16)

where t (min) is the time that the bubble needs to cover a volume V (ml), Tcal

(K) and Texp (K) are the temperature conditions of the calibration and of the

experiment respectively, Pcal (atm) is the pressure conditions during the

calibration (i.e. atmospheric pressure) and Ps (atm) is the saturation pressure

of water at the temperature conditions of the experiment. The calibration


Page 73

lines of the two mass MFCs are shown in the Appendix (Figure A. 1-Figure

A. 2).

Analysis of the gas stream was performed online by means of gas

chromatography. Specifically, a capillary column HP-PLOT Q was used for

the analysis of the gas stream (CO2/N2). GC conditions with this column

were optimised in order to achieve a good separation of the components and

the final conditions chosen are shown in the Appendix (Table A. 1).

The calibration of carbon dioxide was performed, using a 20 vol% CO2/N2

and a N2 cylinder. The concentrations of the gases were calculated by means

of the two calibrated mass flow controllers. The calibration curve of CO2 is

shown in the Appendix (Figure A. 9). It should be noted that in order to

produce accurate experimental results, the GC was calibrated for the carbon

dioxide every day with reproducibility approximately 7%.

3.3.1 Reaction Quench

As the reaction can take place at room temperature and at atmospheric

pressure, quick quench of the reaction is required in order to avoid reaction

downstream of the reactor, so that analysis is accurate. Quench of the

reaction is based on the quick separation of the gas-liquid mixture that exits

the reactor, ensuring also that the extent of the reaction inside the separator

is negligible.

In reaction systems where a basic reactant is involved (e.g. carbon dioxide

into a sodium hydroxide solution), a common way to quench the reaction is

with adding a strong acid (e.g. hydrochloric acid). In this way, salt (from the

reaction between the base and the acid) and water will be produced and the

reaction will stop. However, quenching the carbon dioxide absorption in a

buffer solution of sodium carbonate-bicarbonate with hydrochloric acid was

found to be ineffective. The quench was producing carbon dioxide and

consequently was impossible to identify how much carbon dioxide was


Page 74

consumed due to the reaction and how much was produced due to the

quench. Hence, it was impossible to analyse accurately the reaction system

with this kind of quench.

Different types of gas-liquid separators were also evaluated. Initially, an

open-phase separator (Figure 3.6) was added after the reactor to separate the

exiting gas-liquid stream. This type of separator has been used by many

researchers in the literature [99,157,158] for the same reaction system. The

gas was escaping to the atmosphere, while the liquid was being collected

and analysed by titration with standardised hydrochloric acid.

Figure 3.6 Schematic of open-phase gas-liquid separator.

The disadvantage of this method is that is not a continuous way of analysis

and because the liquid flowrates were very small (Ul<0.03ml/min), it was

taking too long to collect an appreciable amount of liquid sample. This led to

further inaccuracies due to interaction of the liquid with the atmosphere.

Another way to separate the gas-liquid stream after the reactor was to use a

glass separator, which consists of a filter disk with small pores. As the two-

phase fluid enters the separator, the gas is repelled by the hydrophilic pores

while the liquid is forced through the pores via pressure gradient. A glass

separator with a filter disk with pores in a range of 10-16μm was installed

after the capillary reactor. The volume inside the separator (above the filter)

is approximately 2.5ml and its design characteristics are shown in Figure 3.7.


Page 75

Figure 3.7 Schematic of the design characteristics (left) and photograph (right) of

the glass gas-liquid separator with a porous filter inside.

After the separator, the gas was analyzed by means of the GC. It was found

that the gas-liquid stream is separated effectively for gas and liquid

flowrates 1-3ml/min and 0.003-0.05ml/min respectively. However, results of

some blank tests with water showed that physical absorption of carbon

dioxide in water taking place inside the separator was underpredicted by the

corresponding Henry’s constant available in the literature. Consequently, it

was not feasible to close the carbon balance of the system as the amount of

dissolved carbon dioxide in water couldn’t be neither measured nor

calculated based on theory. This was not caused due to leaks in the system,

as leak test was conducted by pressuring the system and no leaks were

found. Therefore, it was impossible to quantify accurately the extent of the

reaction inside this type of separator. Consequently, when using gas-liquid

separators for the analysis of a gas-liquid reaction system, it is of crucial

importance to ensure that no reaction takes place inside the separator.

Another way to analyse carbon dioxide absorption in a carbonate:

bicarbonate buffer solution is to monitor the pH of the liquid phase after the

reactor. As the reaction proceeds, carbonate is being consumed while

bicarbonate is being produced, resulting to a decrease in the pH of the liquid

phase. The stoichiometry of the model reaction can be found in Table 3.1. In

this method the pH of the liquid phase is measured initially (pH0) and then

gas

gas + liquid

liquid


Page 76

is monitored after the reactor (pH1). The pH difference is related to the

conversion of carbon dioxide via (3.17)-(3.18).

𝛽𝑐 =

𝐹𝐶𝑂32−

0 − 𝐹𝐶𝑂2

0,ℓ 𝑋𝐶𝑂2


0 + 2𝐹𝐶𝑂2

0,ℓ 𝑋𝐶𝑂2

⇒ 𝑋𝐶𝑂2=

𝛽𝑐0 − 𝛽𝑐

2𝛽𝑐 + 1∙

𝐹𝐶𝑂32−

0

𝛽𝑐0 ∙

1

𝐹𝐶𝑂2

0,ℓ (3.17)

𝛽𝑐 =[𝑂𝐻−]

𝐾𝑓=

110𝑝𝑂𝐻

𝐾𝑓=

11014−𝑝𝐻

𝐾𝑓⇒ 𝛽𝑐 =

1

𝐾𝑓 ∙ 1014−𝑝𝐻 (3.18)

Where 𝛽𝑐 is the ratio of the carbonate over the bicarbonate concentration,

is the inlet molar flowrate of the carbonate, the inlet molar

flowrate of the bicarbonate, 𝐹𝐶𝑂2

0,ℓ the inlet molar flowrate of carbon monoxide

in the liquid, the conversion of CO2. Finally, 𝐾𝑓 is the equilibrium

constant for the reaction between the carbonate and the bicarbonate, which

can be also defined as the ratio of the second dissociation constant of

carbonic acid and the dissociation constant of water. At 20oC the value of fK

is 41.7 10 /mol [5].

The accuracy of this method of analysis depends on the accuracy of the pH

meter. The pH meter used had 0.01 accuracy, which is translated to

conversion accuracy up to 2% .

However, separation of the gas-liquid stream and then analysis of the gas

stream with gas chromatography would be a much more accurate method

and hence we focused finding the most suitable gas-liquid separator, which

in our case seemed to be microseparators, due to the small volume used in

our system. One of its advantages is the very small gas-liquid interfacial area

it provides due to its small dimensions. Therefore, the extent of the reaction

inside this type of separator can be considered negligible which is very

important for the accurate study of the model reaction.

23

0

COF

3

0

HCOF

2COX


Page 77

3.3.1.1 Experimental Evaluation of Glass-Silicon Microseparators

Microseparators are devices that have been used widely the last decade for

the separation of gas/liquid and liquid/liquid phases based on surface

forces and associated with capillary phenomena [159-169]. Typically they

consist of a main microchannel that is connected to series of small capillaries.

Based on the capillary pressure the non-wetting phase (gas) does not pass

through the capillaries but leaves the microseparator through the main

channel while the wetting phase (liquid) fills the capillaries leading to

efficient separation of the two phases.

In this study, preliminary testing of silicon-glass microseparators was

performed to ensure efficient and stable separation of the gas-liquid stream

exiting the reactor. The efficiency of separation in these devices was tested in

a range of inlet flowrates by controlling the pressure difference across the

capillaries. A detailed study on the performance of these silicon-glass

microseparators was presented recently by Roydhouse et al. [170].

Gas/liquid mixture was entering from the inlet into a 300μm deep

microchannel and then the liquid was being sucked by the 70 capillaries of

40μm wide and 100μm length from both sides (each side consists of 35

capillaries) while the gas was passing across them and was exiting from the

gas outlet (Figure 3.8).

Figure 3.8 Photograph (left) and schematic (right) of the silicon gas-liquid microseparator with etching depth 300μm.

Gas-liquid inlet

Gas outlet

Liquid

outlet Gas-liquid inlet

Liquid outlet

Liquid outlet

Gas outlet

capillaries


Page 78

Details on the fabrication procedure of the microseparators used are given in

the Appendix H.

For the control of the differential pressure across the capillaries, two

metering valves were used at the outlet of the gas and the liquid phase. After

the separator the gas stream was analyzed by gc analysis. The schematic of

the set-up used for the evaluation of the microseparator is shown in Figure

3.9. Separation was evaluated for gas and liquid flowrates 2ml/min and

6μl/min respectively.

Figure 3.9 Schematic diagram of the experimental set-up for the test of the performance of the glass microseparator (Mikroglas).

Microseparators with different etching depths (40, 100, 300, 480μm) were

tested. Wafers with the small etching depth (40, 100μm) were found not

suitable, as they were leaking from the fitting of the inlet, possibly due to

high pressure drop that was developed. Wafers with large etching depth

480μm were also found to be inappropriate as they were leaking from the

bottom of the wafer, because of the thin remaining thickness of the wafer

(Figure 3.10). It was concluded that the separator with etching depth 300μm

is the most suitable in our case.

Using the glass-silicon microseparator with the 300μm etching depth

numerous attempts were conducted to separate a 20%CO2-

carbonate/bicarbonate solution.


Page 79

Figure 3.10 Photograph of the microseparator when it was leaking from the bottom of the silicon wafer with etching depth 480μm.

In the beginning of every run, the microseparator was primed with liquid in

order the capillaries to be filled with liquid. Initially, attempts of separating

the gas-liquid stream were performed without reaction (bypassing the

reactor). The gas and liquid flowrates used were 0.3ml/min and

0.003ml/min respectively. After adjusting gradually the metering valves it

was possible to separate the gas and the liquid phases although sometimes

small bubbles were seen in the liquid phase. However, this was not

important because the goal was to prevent liquid flow to the gas exit, since

after the separator the gas was analyzed. Higher gas flowrates were also

used (up to 2ml/min) and the separation was also successful after slight

decrease of the pressure in the gas phase. It was observed that the system

needed around 10min for the flow to stabilize after every adjustment of the

metering valves. However, in all cases instabilities in the performance of the

glass-silicon microseparator over time were observed. These instabilities are

possibly due to instabilities of the pump and due to fluctuations in the

backpressure on the gas outlet created when i.e. liquid was flowing to the

gas outlet.

Another design of the microseparator was also tried, similar with the one

presented earlier but with only one arm for the liquid stream, hence

containing only 35 capillaries, but its behaviour was similar with the

previous one and the separation was still unstable. Therefore, due to the

instabilities this type of microseparators was not pursued further.


Page 80

3.3.1.2 Design and Evaluation of Glass Microseparator

A glass microseparator was manufactured by Mikroglas (Mainz, Germany)

and its separation efficiency was tested for different gas and liquid flowrates.

Specifically, the aim of this study was to establish operating conditions

under which complete and stable separation of the gas-liquid mixture exiting

the reactor can be achieved. The set-up used for the evaluation of the glass

microseparator was the same as the one used in Chapter 3.3.1.1 (Figure 3.9).

The gas/liquid mixture enters from the inlet into a 200μm deep and 600μm

wide microchannel and then the liquid (DI water) is being sucked due to

capillary forces by the 80 rectangular capillaries of 50μm wide, 200μm deep

and 7700μm length from both sides (each side consists of 40 capillaries)

while the gas (20% CO2) passes across them and exits from the gas outlet

(Figure 3.11). For the precise control of the differential pressure between the

two phases, two metering valves were used at the outlet of the gas and the

liquid phase (Figure 3.9).

Figure 3.11 Photograph of the glass gas-liquid microseparator (mikroglas).

The design characteristics of the microseparator are shown in Figure 3.12.

More photos of the experimental set-up can be found in the Appendix B.

Gas (20% CO2) and liquid (DI water) flowrates ranged between 0.06-

2ml/min and 0.005-0.2ml/min respectively (Table 3-4). A differential

manometer (up to 200kPa) was used in order to monitor the pressure

difference between the gas and the liquid phase and was placed in the gas

and liquid exits before the corresponding metering valves.


Page 81

Figure 3.12 Technical drawing of the glass microseparator (Mikroglas) showing its design characteristics

Table 3-4 Operating conditions of the glass microseparator test and observations.

Fg (ml/min) Fℓ (ml/min) Observations

2 0.005 Complete separation at ΔP=Pgas-Pliquid=1kPa

0.06 0.02 Successful separation at ΔP=0.5-1.5kPa

Rarely pressure fluctuates and bubbles enter the

liquid phase (≈1bubble/10min)

No liquid in the gas phase

Gas breakthrough at ΔP≈2.2kPa

0.06 0.03 Constant separation (ΔP>0.32kPa)

Gas breakthrough at ΔP≈2.49kPa

0.2 0.02 No liquid in the gas phase

Rarely bubbles enter the liquid phase

Furthermore, in the beginning of every run, the microseparator was primed

with liquid in order the capillaries to become wet and consequently the

liquid to be able to flow through.

In Figure 3.13 the limits of applied pressure difference required for an

efficient separation of a 20%CO2-DI water mixture for certain flowrates at

10oC in the glass microseparator are presented. Specifically, the pressure


Page 82

differences limits were highlighted outside which incomplete separation was

observed. Moreover, these experimentally observed operation limits were

also compared with the theoretically expected ones.

The capacity of a separator is based on the number of the capillaries, their

cross sections and their lengths. Therefore, theoretically independently of the

flow regime, as long as the applied pressure difference does not exceed the

capillary pressure (Pb) in the individual capillaries and the flow rates are

below the design limit, complete separation can be achieved. The

breakthrough pressure (Pb) can be calculated using Young-Laplace equation

(3.19), where γ is the interfacial surface tension between the two fluids

(N/m), and R1, R2 are the radii of curvature for each point at the interface.

(3.19)

For cylindrical pores ( ) (3.19) becomes (3.20),

(3.20)

where θ is the wetting angle and r is the pore radius (m). In addition, for the

case of the breakthrough of the gas (non-wetting phase) to the liquid

(wetting phase) θ=0 and (3.20) becomes,

(3.21)

However, for irregular geometries can be substituted for as it is

shown in (3.25), where p is the perimeter (m) and A the area (m2) of the pore

opening [159] and γH2O=0.7197N/m at 20oC.

(3.22)

21

11

RRPb

cos21 rRR

rPb

cos2

2bP

r

r/2 Ap /

b

pP

A


Page 83

Amador et al. [167] studied the stability and the position of an interfacial

meniscus in cylindrical and polygonal pores and they proposed a model for

the description of this phenomenon. According to them, the position of the

meniscus is moving inside the capillary until the pressure difference across

the meniscus interface becomes equal to Pb.

The second design limit (lower limit) of a microseparator is determined by

the maximum possible flowrate through the capillaries and can be found

using Hagen-Poiseuille’s law which calculates the pressure drop due to the

laminar flow of Newtonian fluid along a length of tubing of known

geometry (3.23),

(3.23)

where, α is a numerical prefactor related to the geometry of the cross section

of the channel, η is the liquid viscosity (ηH20=10-3Pa∙s at 20oC_, Q is the liquid

flowrate (m3/s), L is the channel length (m) and A the cross-sectional area of

the channel (m2). It was reported [171] that α is linearly related to the shape’s

compactness factor, C (C=perimeter2/area) for a channel of any geometry

cross-section. For a pore with rectangular geometry,

𝛼 =

22

7𝐶 −

65

3 (3.24)

Significant deviation was observed between the theoretically predicted gas-

to-liquid breakthrough pressures (by Young-Laplace equation) and the

experimentally observed ones. This behaviour was also observed by

Roydhouse et al. [170] who studied the breakthrough pressures of capillary

microseparators. They showed that at low flowrates the experimental gas-to-

liquid pressures were in qualitatively agreement with the theoretical ones,

while at higher flowrates deviations were significant. TeGrotenhuis et al.

[161] also observed gas breakthrough at pressure differences below the

Young-Laplace pressure limit, Pb, of the pore throat when studying the gas-

liquid separation in a single-channel microchannel which employs a pore

2A

QLP


Page 84

throat within it. The deviation in that case was explained due to fluctuations

in the backpressure in the gas outlet that were significant when liquid was

flowing to the gas outlet.

Figure 3.13 Operating conditions of the glass microseparator consisting of 80 capillaries, illustrating minimum applied pressure difference required to remove all

the liquid from the gas-liquid stream (grey line), applied pressure difference at which gas breakthrough occurs (black line) and experimentally observed gas (black dots)

and liquid (grey dots) breakthrough.

It was concluded that for small liquid flowrates (up to 0.3ml/min) complete

and stable separation is possible even for very high gas to liquid ratios (e.g.

flowrates gas: liquid=400) after adjusting the pressure difference between the

gas and the liquid phase (ΔP=Pgas-Pliquid) by means of two metering valves

between 0.3-2kPa. For ΔP below 0.3kPa, the capillaries were not able to suck

all the liquid. Therefore, liquid was observed flowing to the gas exit. On the

other hand, for ΔP above 2.5kPa, gas was breaking through the capillaries

and was flowing to the liquid exit. For larger liquid flowrates (bigger than

0.3ml/min) pressure fluctuations were observed, resulting to an unstable

system (either gas or liquid breakthrough). In conclusion, the glass

microseparator seems the most promising way to separate the gas-liquid

reaction mixture for the study of quench of the reaction as only small liquid

flowrates are needed.


Page 85

3.3.2 Hydrodynamic Study of Gas-Liquid Flow

For the kinetic study of a system the hydrodynamic study of the system is

essential as it provides information on the mass transfer characteristics of the

system, the reaction volume and time and the mixing quality of the system.

This is crucial especially in gas-liquid systems where depending on the gas

and liquid flowrates different flow patterns are observed and depending on

the flow pattern, the system presents very different hydrodynamic and mass

transfer characteristics.

Observation of the gas-liquid flow system was performed by means of a

high-speed camera (Phantom Miro 4) under different gas (20%CO2-N2) and

liquid (sodium carbonate: bicarbonate buffer solution) flowrates in two

circular glass tubing with inner diameters 1mm and 0.5mm. The

corresponding schematic of the experimental set-up is shown in Figure 3.14.

Figure 3.14 Schematic diagram of the experimental set-up for flow observation of the gas-liquid flow by means of a high-speed camera.

It should be mentioned that the part of the tubing that was recorded by the

camera was immersed in water medium to minimise the beam steering effect

of the curved tube wall [78].

In Figure 3.15 it is clear that when the tubing is not immersed into the water

medium, is difficult to determine the wall thickness and therefore the use of


Page 86

a water medium to immerge the tubing is quite crucial for the accuracy of

the flow observation.

Figure 3.15 Images of the glass circular tubing (ID=1mm) without water medium (left picture) and with water medium (right picture) under Fg=1.6ml/min and

Fl=0.006ml/min).

The operating conditions of the flow observation experiments together with

the results are shown in Table 3-5.

Table 3-5 Conditions and results of flow observation and calculation of mass transfer coefficient, kℓα and Hatta number at 0.03ml/min liquid flowrate.

Exp T oC

ID

mm

υg

ml/min

Lbubble

cm

Lliquid slug

cm

Film

thickness

µm

kℓα

s-1 Ha0 Haf

1 20 1 0.3 0.8-1 0.035-0.038 <<30 0.36 0.08 0.05

2 20 1 0.5 1.1-1.2 0.03-0.04 30 0.37 0.08 0.05

3 20 1 1 2.5-2.6 0.029-0.038 36 0.36 0.08 0.05

4 20 1 2 5.8-6.3 0.018-0.030 45 0.37 0.08 0.05

5 10 1 0.3 0.8-0.1 0.035-0.038 <<30 0.35 0.05 0.04

6 10 1 0.5 1.1-1.2 0.03-0.04 30 0.36 0.05 0.04

7 10 1 1 2.5-2.6 0.029-0.038 36 0.35 0.05 0.04

8 10 1 2 5.8-6.3 0.018-0.030 45 0.35 0.05 0.04

9 20 0.5 0.3 4-5 0.1-0.2 - 0.67 0.08 0.07

10 20 0.5 0.5 9-11 0.1-0.2 - 0.68 0.08 0.07

11 20 0.5 1 15-17 0.1-0.2 - 0.7 0.08 0.07

12 20 0.5 2 30-35 0.1-0.2 - 0.71 0.08 0.07

The gas and the liquid flowrates ranged between 0.1-3ml/min and 0.006-

0.01ml/min respectively. Under these gas and liquid flowrates, slug and slug

annular flow were observed, as defined in Chapter 2.3.1.


Page 87

It can be seen that as the gas flowrate increases the bubble length increases

significantly while the liquid slug length slightly decreases. Bubble lengths

found also to increase when capillary size decreases. These observations

have found to be in good agreement with the literature [172,173].

Furthermore, the liquid film around the gas bubble flowing at 20oC found to

become thicker when the gas flowrate increases (and hence as the capillary

number increases in a range between 0.001-0.003). This is consistent with

previous observations of Taylor’s and Bretherton’s first experiments

[174,175]. Due to limitation of the current equipment, it was not feasible to

measure the film thickness at very small flowrates and using the capillary

with 0.5mm inner diameter.

The mass transfer coefficient was estimated by means of van Baten and

Krishna’s correlation for long contact times (3.22), as it was found that under

these operating conditions Fo>1 based on (3.26).

(3.25)

(3.26)

where D is the diffusion coefficient of the gas in the liquid, t is the contact

time between the two phases and d is the diffusion path length of the liquid

which in our case is equal with the film thickness.

Hatta number was calculated based on (2.4), assuming that the gas film

resistance is negligible,

𝐻𝑎 =


𝑘ℓ (3.27)

where 𝑘𝑟 is the reaction rate constant of the reaction, 𝐷 is the reactant A

diffusivity into the liquid and 𝑘ℓ the mass transfer coefficient of A in the

liquid phase.

, ,

42 42 3.41

gBcap cap film film

UC film

Du Dk k k

d L d

2

D tFo

d


Page 88

Hatta number was calculated both in the inlet (Ha0) and outlet of the reactor

(Haf) as it was shown that the reaction rate constant changes along the

reactor and hence Hatta number changes as well along the reactor. It was

found that kℓα in this range of conditions is between 0.35-0.71s-1 depending

on the gas and the liquid flowrates. Moreover, Hatta number was found that

ranges between 0.04-0.08, indicating that the mass transfer resistances in this

system are negligible based on Hatta criterion (Ha<<0.3, as explained in

Chapter 2.1.3).

3.3.3 Residence Time Distribution Experiments

Residence time distribution experiments were performed in order to

measure the liquid residence time and the liquid volume fraction of the

system under conditions similar to reaction experiments. Experimental RTD

measurements were performed by monitoring the concentration of a tracer

dye by means of a LED-photodiode system. Experiments were performed

with pure nitrogen and a 0.1M sodium carbonate: bicarbonate (1:9) solution

in a glass capillary with 1m length and 1mm inner diameter.

The set-up used (Figure 3.16) has been described by Cantu-Perez et. al [114]

in the past. The tracer pulse (Parker Blue dye) was introduced by a 6-port

sample injection valve (Rheodyne 7725(i)) equipped with 0.3ml sample loop

and an internal position signal switch that indicated the time of injection.

The piping among all components was PFA 1mm ID. Tracer detection was

performed by light absorption in the inlet and in the outlet of the glass

reactor. Illumination was provided by two square LEDs (Kingbright L-

1553IDT). To seal the system from ambient light it was placed in a dark box.

The detection system was based on a linear diode array detector (TSL,

1401R-LF) which had 128 diodes each of dimensions 63.5μm by 55.5μm. This

was driven using the manufacturer’s recommended circuit. A scan of all

diodes would take 128μs and the interval between successive scans was

5.12μs.


Page 89

Figure 3.16 Schematic of experimental set-up for RTD study of model system.

Data from the sensor was collected using a National instruments PCI-6010

data acquisition card before being analysed and displayed on a computer

using a program written in Labview. Every 100ms the computer would

average the previous two scans, calculate the absorbance for each diode and

display the result.

Validation of the method used for the analysis of the RTD experiments can

be found in the Appendix (Appendix D) where the analysis methodology of

the signal is also demonstrated. The method was firstly validated by

analysing the RTD curves of liquid-only flows where the residence time of

the fluid was known (𝜏 = 𝑉𝜐ℓ

⁄ ).

The RTD curves for various gas-to-liquid ratios are presented in Figure 3.17

where by decreasing the gas-to-liquid ratio the RTD curve becomes sharper

indicating a plug-like behaviour.


Page 90

Figure 3.17 RTD curves for a range of gas-to-liquid ratios.

All the finding of the RTD experiments are summarised in Table 3-6.

Table 3-6 Results of RTD experiments for various gas-to-liquid ratios conditions.

υg

(ml/min)

υℓ

(ml/min)

gas-liquid

ratio

τℓ

(s) D/uL A

0.5 0.5 1 53.4 0.00006 0.8

1 0.5 2 39.5 0.0004 0.83

2 0.5 4 28.4 0.005 0.85

3 0.5 6 17.7 0.005 0.88

0.3 0.03 10 254 0.02 0.91

2 0.03 66 118 0.08 0.93

In Table 3-6 υg, υℓ are the gas and the liquid flowrates, τℓ is the

experimentally measured liquid residence time, D/uL is the dispersion

number and A is the numerical prefactor found to satisfy (3.28),

휀𝑔 = 𝐴 ∙

𝑗𝑔

𝑗𝑔 + 𝑗ℓ (3.28)


Page 91

Factor A in the case of Armand’s model is equal to 0.833 while in the case of

homogenous model is equal to 1. The reproducibility of the system was

satisfactorily with uncertainty of ±3% concerning the mean residence time of

the liquid.

As the gas to liquid ratio increases the dispersion number, , is also

increasing (Table 3-6), behaviour which was also observed by Zhang et al.

[118]. They studied the effect of temperature, pressure and flow pattern on

the observed RTD of a toluene/nitrogen and a cyclohexane/nitrogen system

at gas-to-liquid-ratios between 0.3-0.005 in a stainless steel tube with 2mm

inner diameter and reported increasing deviation from plug flow behaviour

when increasing the gas flowrate or decreasing the liquid flowrate. Higler et

al. [176] observed also the same effect of the gas-to-liquid ratio on the RTD

curves when measuring the liquid-phase residence time of an air-water

system in structured packed columns of 10-24cm inner diameter.

Moreover, in our system it was observed that when the ratio becomes 10

then indicating that the flow starts deviating from the ideal plug

flow behaviour.

Another point worth noting in Table 3-6 is that as the gas to liquid ratio

increases the factor A gradually increases. For gas-to-liquid ratios below 3

Armand’s model can be used while for ratios above 10 it would be better to

use the homogenous model. However, these results highlight the necessity

of actually measuring the residence time and the void fraction of a gas-liquid

system experimentally instead of using correlations. One should be very

careful when using these void fraction correlations if using a channel with

different geometrical characteristics, different fluids or different gas-to-liquid

ratios.

D uL

0.01D uL


Page 92

3.4 Reactor Model

3.4.1 Reactor Model Development

A simple one-dimensional plug-flow reactor model was developed to

simulate the carbon dioxide absorption in buffer solutions in capillary

reactors and it will be further used for the kinetic study of

methoxycarbonylation of ethylene. It was aimed to keep the reactor model at

a lower level of complexity in order to reduce the time required to run the

simulation and the number of parameters which need to be determined. The

differential volume element considered for the modelling is shown in Figure

3.18 and consists of a cylindrical part with outer diameter equal with the

inner diameter of the capillary, d, thickness equal with the liquid film

thickness, δ, and length equal with a distance element dx.

Figure 3.18 A volume element ΔVℓ in the liquid phase in a gas-liquid reactor

An annular-type flow is assumed where the liquid is flowing along the walls

of the tube while the gas is flowing in the core. In the gas-liquid interphase it

is assumed that vapour-liquid equilibrium is established between the two

phases for each component. The reaction takes place only in the liquid phase.

The reactor model considers the mass balances in the gas and the liquid

phase.

The assumptions considered are the following:

Plug flow in the gas and the liquid phase Steady state, isothermal reactor Reaction takes place only in the liquid phase


Page 93

Equilibrium at the gas-liquid interface Constant gas and liquid volumetric flowrates along the reactor

The mass balance for the CO2 in the liquid phase for a volume element ΔVℓ

in the liquid phase can be written as,

𝑙𝑖𝑞. 𝑓𝑙𝑜𝑤, 𝑖𝑛 − 𝑙𝑖𝑞. 𝑓𝑙𝑜𝑤, 𝑜𝑢𝑡 + 𝑖𝑛 𝑏𝑦 𝑎𝑏𝑠𝑜𝑟𝑝𝑡𝑖𝑜𝑛 − 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛 = 0 (3.29)

𝐹𝐶𝑂2

ℓ

|𝑉ℓ − 𝐹𝐶𝑂2

ℓ

|𝑉ℓ+∆𝑉ℓ + 𝑁𝐶𝑂2

ℓ ∆𝐴 − 𝑟𝐶𝑂2∆𝑉ℓ = 0 (3.30)

By defining the volume fraction of the liquid, , as well as the ratio, α,

휀ℓ =

∆𝑉ℓ

∆𝑉𝑟=

𝑙𝑖𝑞𝑢𝑖𝑑 𝑣𝑜𝑙𝑢𝑚𝑒 𝑒𝑙𝑒𝑚𝑒𝑛𝑡

𝑟𝑒𝑎𝑐𝑡𝑜𝑟 𝑣𝑜𝑙𝑢𝑚𝑒 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 (3.31)

𝛼 =

∆𝐴

∆𝑉𝑟=

𝑖𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑖𝑎𝑙 𝑐𝑜𝑛𝑡𝑎𝑐𝑡 𝑎𝑟𝑒𝑎

𝑟𝑒𝑎𝑐𝑡𝑜𝑟 𝑣𝑜𝑙𝑢𝑚𝑒

(3.32)

Equation (3.30) can be written as,

𝐹𝐶𝑂2

ℓ

|𝑉ℓ+∆𝑉ℓ − 𝐹𝐶𝑂2

ℓ

|𝑉ℓ = 𝑁𝐶𝑂2∙ℓ 𝛼 ∙ ∆𝑉𝑟 − 𝑟𝐶𝑂2

∙ 휀 ∙ ∆𝑉𝑟 = 0 (3.33)

After division by the reactor volume element rV and allowing 0rV ,

𝑑𝐹𝐶𝑂2

ℓ

𝑑𝑉𝑟= 𝑁𝐶𝑂2

ℓ ∙ 𝛼 − 𝑟𝐶𝑂2∙ 휀 (3.34)

The molar flowrate of CO2 in the liquid phase 2COF and the volume element

𝑉ℓ can be expressed by,

𝐹𝐶𝑂2

ℓ = 𝑗ℓ ∙ 𝐴𝑐 ∙ 𝐶𝐶𝑂2

ℓ (3.35)

𝑑𝑉ℓ = 𝐴𝑐𝑑𝑥 (3.36)

where j is the superficial velocity of the liquid, Ac is the tube cross section

area.


Page 94

Equation (3.34) is now transformed to,

𝑗ℓ

𝑑𝐶𝐶𝑂2

ℓ

𝑑𝑥= 𝑁𝐶𝑂2

ℓ 𝛼 − 𝑟𝐶𝑂2∙휀ℓ (3.37)

The reaction 2COr can be expressed by (3.38) (see Chapter 3.2),

𝑟𝐶𝑂2= 𝑘𝑟 ∙ 𝐶𝐶𝑂2

ℓ (3.38)

The reaction rate constant 𝑘𝑟 depends on the reaction temperature and the

ratio of carbonate and bicarbonate concentrations.

The flux of CO2 from the liquid film to the liquid bulk 2CON is obtained by

(3.39),

2 2 2

,i

CO CO CON k C C (3.39)

where is the mass transfer coefficient in the liquid phase, is the

concentration of the liquid CO2 in the gas-liquid interface and is the

concentration of the liquid CO2 in the bulk of the liquid.

The boundary condition of (3.37) is that in the inlet of the reactor all the

carbon dioxide is in the gas phase and hence,

2

0 0COx C (3.40)

Similarly, the mass balance for the CO2 in the gas phase for a volume

element ΔVg (

Figure 3.19) in the gas phase is expressed by,

𝑔𝑎𝑠 𝑓𝑙𝑜𝑤, 𝑖𝑛 − 𝑔𝑎𝑠 𝑓𝑙𝑜𝑤, 𝑜𝑢𝑡 − 𝑜𝑢𝑡 𝑏𝑦 𝑎𝑏𝑠𝑜𝑟𝑝𝑡𝑖𝑜𝑛 = 0 (3.41)

k2

,i

COC

2COC


Page 95

2 2 2

0g g g

g g g

CO CO COV V VF F N A

(3.42)

Figure 3.19 A volume element ΔVg in the gas phase in a gas-liquid reactor.

Substituting (3.32) into (3.42),

2 2 2

g g g

g g g r

CO CO COV V VF F N V

(3.43)

Where Vg is the volume occupied by the gas phase while Vr is the total

volume of the reactor.

After division by the reactor volume element rV and allowing 0rV ,

2

2

g

CO g

COr

dFN

dV (3.44)

Substituting for gas superficial velocity, equation (3.44) becomes,

2

2

g

COg g

CO

dCj N

dx (3.45)

The flux of CO2 from the gas bulk to the gas film 2

g

CON is defined by (3.46),

2 2 2

,g g g i

CO g CO CON k C C (3.46)

where is the mass transfer coefficient in the gas phase, is the

concentration of the gas CO2 in the gas-liquid interface and is the

concentration of the gas CO2 in the bulk of the gas.

The boundary condition at the inlet is,

gk2

,g i

COC

2

g

COC


Page 96

2

2 2

,00COg g

CO CO

y Px C C

RT (3.47)

At the gas-liquid interface, a chemical equilibrium is assumed to exist and

the concentrations of the carbon dioxide in the gas and in the liquid phase

are related to each other by (3.48), where 2COK is the equilibrium constant

[177].

2

2

2

,

,

g i

CO

CO i

CO

CK

C (3.48)

The unknown concentration of carbon dioxide in the interface can be

calculated by (3.49).

2 2

g

CO CON N

2 2 2 2 2

, ,g i i

g CO CO CO CO COk C K C k C C (3.49)

Assuming that the resistance in the gas film is negligible compared to that in

the liquid film, the fluxes of carbon dioxide in the gas and the liquid film are

expressed by (3.50). This assumption is valid as the diffusion coefficient of

carbon dioxide in the gas phase is much bigger than that in the liquid phase.

2

2 2 2

2

g

CO g

CO CO CO

CO

CN k C N

K

(3.50)

At the interface the Henry’s law is given by (3.51),

𝐶𝑖ℓ

𝐶𝑖𝑔 = 𝐾𝑖 =

𝑅𝑇

𝐻𝑖 (3.51)

where 𝐾 is the Henry’s law constant defined as the ratio of liquid to gas

concentrations [7] and H is solubility.

The model equations (3.37)-(3.40),(3.45)-(3.47) and (3.50) were solved using

Polymath software. The parameters involved in the model are listed in Table


Page 97

3-7 together with the correlations used for their determination or reference

values.

Table 3-7 Model parameters and relevant correlations

Parameter Units Correlation/Value

s-1

van Baten and Krishna [105]:

- Armand [108]: 휀𝑔 = 𝐴𝑗𝑔

𝑗𝑔+𝑗ℓ

𝑚𝑜𝑙 𝐿 ∙ 𝑎𝑡𝑚⁄

= 0.05 at 10oC

= 0.037 at 20oC [156]

kr - 𝑘𝑟 = 0.21 ∙ 𝛽𝑐 𝑎𝑡 10 𝐶𝑜

𝑘𝑟 = 0.56 ∙ 𝛽𝑐 𝑎𝑡 20 𝐶𝑜 [141]

3.4.1.1 Model Sensitivity on Mass Transfer Coefficient

The effect of the mass transfer coefficient on the overall performance of the

model system was studied using the suggested reactor model. Keeping the

gas flowrate constant (Ug=0.1ml/min), different cases were studied with

different liquid flowrates and operating conditions. In all cases, the

corresponding reactor had a length of 1m and an inner diameter of 0.5mm

and the operating conditions of the carbon dioxide (20 vol% CO2/N2)

absorption in a 0.1M sodium carbonate bicarbonate solution were 10oC and

1atm. Different values of kℓα were used while keeping all the other

parameters the same.

In Figure 3.20 the effect of the mass transfer on the conversion of carbon

dioxide is shown. It can be seen that the effect of the mass transfer on the

reaction rate is insignificant and it only starts affecting the reaction rate when

kℓα is lower than 0.1s-1. It should be noted that during experiments, kℓα was

calculated to be around 0.35s-1, as shown in Chapter 3.3.2. Therefore, it can is

ensured that the experimental results of the model reaction were intrinsic

kinetic data.

k , ,

42 42 3.41

gBcap cap film film

UC film

Du Dk k k

d L d

2COK2COK

2COK


Page 98

Figure 3.20 Conversion of carbon dioxide reaction against volumetric liquid mass transfer coefficient for different liquid (Na2CO3:NaHCO3 (1:9)) flowrates under

constant gas (20% CO2) flowrate (Ug=0.1ml/min) at 10oC, at atmospheric pressure in a capillary reactor with L=1m, ID=0.5mm.

3.4.1.2 Liquid Volume Fraction

In Figure 3.21 the effect of the liquid volume fraction, εℓ, on the predicted

conversion of carbon dioxide is shown under the same operating conditions

as previously. The model uses Armand correlation to calculate the liquid

volume fraction and under these conditions (Ul=0.02ml/min, Ug=0.1ml/min

at 10oC) the predicted value was 0.305. Two different values of εℓ (0.25 and

0.35) were used to investigate the effect of a small deviation from the

Armand correlation on the accuracy of the model. In Fig.3.5 it is shown that a

moderate deviation (~15%) from the Armand correlation produces a

noticeable change (~10%) in the predicted conversion. Since it was shown

earlier that Armand correlation cannot be applied for gas-to-liquid ratios

larger than 2, the importance of measuring experimentally the liquid void

fraction is highlighted, so it is determined with better accuracy.


Page 99

Figure 3.21 Effect of liquid volume fraction on conversion of carbon dioxide predicted from the model (Ug=0.1ml/min 20% CO2, Ul=0.02ml/min

Na2CO3:NaHCO3 (1:9) at 10oC) in a capillary reactor (L=1m, ID=0.5mm).

3.4.2 Comparison of Model with Experimental Results

Initially blank tests were conducted using 2% CO2/DI water in order to

compare the experimental measured physical absorption with the theoretical

one. As CO2 solubility into water at 20oC is 0.039kmol/m3atm, for gas and

liquid flowrates 0.5ml/min and 0.03ml/min the maximum expected

absorption of CO2 is around 6.1%. Under the same conditions, the

experimental measured absorption of CO2 was found to be 5.05% ±0.23 in

good agreement with the model.

Reaction experiments were performed and the corresponding operating

conditions are shown in Table 3-8 together with the experimental results and

the corresponding predictions of the reactor model.


Page 100

Table 3-8 Experimental results of the model reaction and corresponding model predictions under different operating conditions when inlet liquid

flowrate was constant at 0.03ml/min.

No. T Reactor υg 𝜺𝓵 Conversion %

Exp. (oC) ID (mm)

L (m)

(ml/min) model experiment

1 20 1 1 0.3 0.17 69.31 73.33

2 20 1 1 0.5 0.13 46.9 40.62

3 20 1 1 1 0.10 25.15 22.97

4 20 1 1 2 0.08 12.92 13.1

5 10 1 1 0.3 0.17 53.28 49.405

6 10 1 1 0.5 0.13 34.67 30.33

7 10 1 1 1 0.10 18.16 19.83

8 10 1 1 2 0.08 9.23 10.48

9 20 0.5 1 0.3 0.17 36.76 40.75

10 20 0.5 1 0.5 0.13 23.05 25.15

11 20 0.5 1 1 0.10 11.75 12.79

12 20 0.5 1 2 0.08 5.71 6.21

In Figure 3.22 the experimentally observed carbon dioxide conversion in a

glass reactor of 1m length and 1mm inner diameter at 20oC is plotted against

the liquid residence time (as measured in residence time experiments). The

residence time varied between 2-4.5min by decreasing the gas flowrate while

keeping the liquid flowrate fixed (Table 3-8).The conversion of carbon

dioxide increases when liquid residence time increases as more time is

available for the reaction to take place. The experimental results of carbon

dioxide conversion are also compared with the corresponding predictions of

the reactor model (bold line in Figure 3.22) and a good fit between the two is

shown. Any deviations between the model predictions and the experimental

results can be attributed to the experimental error observed (≈8%).


Page 101

Figure 3.22 Experimental results and model predictions for Fg=0.3-2ml/min, Fl=0.03ml/min at 20oC in a glass reactor of 1m length and 1mm inner diameter (No.

experiments=1-4).

Similarly, in Figure 3.23 the experimentally observed carbon dioxide

conversion in a glass reactor of 1m length and 1mm inner diameter at 10oC is

plotted against the liquid residence time.

Figure 3.23 Experimental results and model predictions for Fg=0.3-2ml/min, Fl=0.03ml/min at 10oC in a glass reactor of 1m length and 1mm inner diameter (No.

experiments=5-8).


Page 102

Lower carbon dioxide conversion is observed at higher gas flowrate due to

the smaller liquid residence time at higher gas flowrate. Moreover, due to the

lower temperature conditions in this series of experiments, lower

conversions were observed in total compared to those at 20oC in Figure 3.22.

This is due to the higher reaction rate constant at higher temperatures.

Moreover, model predictions provide a good fit of the experimental data in

all cases.

In Figure 3.24 the experimentally observed carbon dioxide conversion in a

glass reactor of 1m length and 0.5mm inner diameter at 20oC is plotted

against the liquid residence time.

Figure 3.24 Experimental results and model predictions for Fg=0.3-2ml/min, Fl=0.03ml/min at 20oC in a glass reactor of 1m length and 0.5mm inner diameter

(No. experiments=9-12).

For the same gas and liquid flowrate, lower carbon dioxide conversions are

observed in Figure 3.24 compared to the corresponding experiments in the

glass reactor with 1mm inner diameter (Figure 3.22). This is due to the

smaller reactor volume that led to smaller residence time of the liquid and

hence less time for reaction to take place resulting to smaller conversions of


Page 103

carbon dioxide. The experimental data are also compared with the

corresponding model predictions presenting satisfactorily fit.

Furthermore, the accuracy of the reactor model to predict the reaction

performance is highlighted in the following parity plot (Figure 3.25) where

the experimentally measured conversions of carbon dioxide for exps.1-12

(Table 3-8) are plotted together with the corresponding model predictions.

Figure 3.25 Parity plot of carbon dioxide conversions for exps.1-12 (Table 3-8) and model predictions.

It is observed that model is satisfactorily predictive in the whole range of

operating conditions as the deviation from the experimental results is always

less than 15%. Hence, it can be concluded that the model is able to predict

satisfactorily the behaviour of the model reaction in different designs of

capillary microreactors as well as at different reaction temperatures and

different residences times.

3.5 Conclusions

The performance of carbon dioxide absorption in a 0.1M

carbonate:bicarbonate (1:9) buffer solution was studied in glass capillary

microreactors of 0.5mm and 1mm inner diameter at different temperature

+15%

-15%


Page 104

conditions and different residence times (by varying the gas flowrate and

keeping the liquid flowrate constant). Reaction analysis was based on the

analysis of the gas stream with gc, after quenching the reaction and

separating the gas-liquid flow using a glass microseparator. Results showed

that carbon dioxide conversion decreases with increasing gas flowrate (while

keeping the liquid flowrate constant) due to the decrease of the liquid

volume fraction (and hence the reaction volume as the reaction takes place

only in the liquid phase). At constant gas and liquid flowrates, higher

conversion of carbon dioxide was observed at higher temperatures due to

the higher reaction rate constant at higher temperature.

Hydrodynamic study of the flow system was also performed and the flow

characteristics, the residence time and the void fraction of the system were

determined based on flow observation and residence time distribution

experiments. The flow pattern under the operated conditions found to be

slug-annular flow with long gas bubbles and thin liquid slugs in between.

Bubble length found to increase with increase of the gas flowrate or with

decrease of the capillary size. Moreover, the liquid film around the gas

bubble found to become thicker when the gas flowrate increases (and hence

as the capillary number increases), consistent with previous observations of

Taylor’s and Bretherton’s first experiments [174,175]. Based on the flow

observation results, the mass transfer characteristics of the system were

determined based on van Baten and Krishna’s correlation and it was

concluded that the system does not suffer from mass transfer limitations

(based on Hatta criterion) but is under kinetic control under the operated

conditions. Furthermore, RTD experiments under different gas-to-liquid

ratios showed that the dispersion number, , increases with gas-to-

liquid ratio, consistent to previous studies [118], [176]. Another point worth

noting is that as the gas to liquid ratio increases the factor A, required for the

theoretical estimation of the void fraction of the system gradually increases.

Specifically, it was found that Armand correlation can be accurately used

D uL


Page 105

only for gas-to-liquid ratios below 3 while for higher ratios experimental

measurement of the void fraction is necessaire.

Furthermore, a mathematical model was developed to simulate the reaction

in the capillary reactor and its validity was confirmed with comparison with

experimental results. The model predicted satisfactorily the experimental

results in the whole range of operating conditions with deviations always

smaller than 15%. Hence, it can be concluded that the reactor model can be

further used for the simulation of other gas-liquid catalytic reaction in

capillary reactors under slug-annular flow.

Page 106

CHAPTER 4. Hydrodynamic Study of Gas-Liquid Flow

Systems in Microcapillaries

4.1 Introduction

When studying multiphase reaction systems, knowledge of the

hydrodynamics of the system is essential as they affect significantly both the

mass transfer and the heat transfer of the system, determining the reaction

yield. The last decade many researchers [68-92] have focused on studying the

hydrodynamics of multiphase systems in microchannels giving significant

insight on the flow patterns, the void fraction and the pressure drop of the

studied systems as well as the factors that affect these. In Table 2-2,

hydrodynamic studies available in the literature on two phase-flow systems

in micro and mini-channels are listed. However, these studies mainly

focused in multiphase systems with moderate gas and liquid flowrates

(jg,jℓ>0.4m/s), while no studies were found for lower gas and liquid

velocities.

The objective of this study is to investigate experimentally the

hydrodynamics of gas-liquid flow systems with very small gas and liquid

superficial velocities (Figure 4.1) in circular microcapillaries. Gas and liquid

superficial velocities were varied between 0.004-0.068m/s and 0.0001-

0.102m/s respectively. Hydrodynamic characteristics such as the flow

pattern, the void fraction and the residence time distribution were

experimentally measured and their dependence on the fluid properties, the

capillary diameter and the gas-to-liquid ratio was investigated. For this

purpose, flow observation and residence time distribution measurements of

various gas-liquid systems such as N2/methanol, N2/water and N2/glycerol

were conducted at a range of gas-to liquid ratios (jg:jℓ=0.66-40) in circular

PFA capillaries with various inner diameters (ID=0.25, 0.5, 1mm).

CHAPTER 4. Hydrodynamic Study of Gas-Liquid Flow Systems in Microcapillaries

Page 107

Figure 4.1 Range of gas and liquid superficial velocities used in this study compared to Triplett et al. [69]study in a 1mm circular capillary.

The experimentally measured void fractions were then compared with

published hydrodynamic models and a new correlation is suggested for the

void fraction of N2/water systems in circular capillaries with inner diameter

0.25-1mm.

4.2 Experimental Set-Up and Operating Conditions

A schematic diagram of the experimental set-up used for the hydrodynamic

study is shown in Figure 4.2. The experiments conducted in circular PFA

tubes with various inner diameters (0.25, 0.5, 1mm) under different gas to

liquid ratios (jg:jℓ=0.66-40) in order to investigate different flow patterns. Gas

was controlled by a mass flow controller (Brooks, T67438/001) while the

liquid was delivered by a syringe pump. A pressure indicator (Comark,

C9555, 0-30psi) was added in the inlet gas side to monitor the pressure

during the experiments. Flow observation of the system was conducted by

means of a microscope camera and the flow characteristics of the gas-liquid

systems such as the liquid slug and the gas bubble length were recorded.


Page 108

Figure 4.2 Schematic of the experimental set-up used for the hydrodynamic study of gas-liquid systems in circular microcapillaries.

Furthermore, residence time distribution (RTD) experiments were conducted

by introducing a step-input change on the liquid feed concentration and

monitoring this change in the inlet and outlet of the reactor. The inlet step-

input change on the liquid feed concentration was created by injecting a

tracer with a syringe via a 6-port valve which was installed after the syringe

pump. The concentration change was being monitored in the inlet and the

outlet of the reactor by two infrared optical sensors. A great benefit of using

IR sensors is that there is no sensitivity to the ambient light hence it is very

easy to use compared to other sensors (e.g. linear diode array detectors)

sensitive to ambient light, where the set-up has to be installed inside a box

that prevents light transmittance (e.g wooden box used in Chapter 3.3.3)

making the handling difficult. In this way, RTD experiments can be

performed simultaneously with reaction experiments, measuring in that way

the real residence time and reaction volume of a system under reaction. This

has many advantages, as it takes into account changes in the flow behaviour

along the reactor due to reaction (e.g decrease of gas flowrate) or flow

anomalies along the reactor (e.g waves), which are not taken into account


Page 109

when studying the hydrodynamics of a system off-line or when using

relative hydrodynamic correlations.

All experiments were conducted at room temperature and atmospheric

pressure. A picture of the experimental set-up is shown in Figure 4.3.

Figure 4.3 Picture of the experimental set-up for the hydrodynamic study of gas-liquid systems in circular microcapillaries.

During the hydrodynamic study working fluids were nitrogen, deionised

water, methanol and 10% aqueous glycerol which physical properties are

shown in Table 4-1.

Table 4-1 Physical properties of working fluids

The gas mass flow controller was calibrated with nitrogen using a bubble

meter at NTP conditions (20oC, 1bar). The calibration results were also

corrected for the moisture effect and the temperature effect based on (3.16).

Fluid Density

3( / )kg m

Viscosity

( )Pa s

Surface Tension

( / )N m

Deionized water 997 0.899 0.0720

Methanol 782 0.256 0.0221

Glycerol (10%) 1021 1.147 0.0705

Nitrogen 1.2 0.0179


Page 110

The calibration line of the mass flow controller is shown in the Appendix

(Figure A. 3).

For the residence time distribution experiments, the choice of the tracer was

based on the sensitivity of the optical sensors on the specific fluid. For this

purpose, the sensors sensitivity for various fluids was plotted against the

refractive index of these fluids. Refractive index is a dimensionless number

and is characteristic to the fluid describing how light propagates through

that fluid (Figure 4.4). A suitable tracer would be one for which the

difference in detector’s output between the main fluid and the tracer is

significantly different.

Figure 4.4 Sensitivity of optical sensor to different components [178].

In order to obtain a clean step signal, toluene was chosen as the tracer when

methanol was the working fluid and 0.3M CuCO4 when 10% aqueous

glycerol was the working fluid.

4.2.1 Residence Time Distribution Experiments: Method Analysis and

Validation

The methodology followed for the analysis of the RTD signal has been

described in detail in Chapter 2.3. In order the analysis methodology

followed to be valid one should ensure that the system is in the dispersion


Page 111

and not the convection region based on Figure 4.5. For this purpose, we

consider the equivalent single phase (liquid only system) with inner

diameter equal with the film thicken and fluid velocity the superficial

velocity of the liquid. Hence, in Figure 4.5 L represents the length of the

reactor (≈80-270cm in this study), dt is the liquid film thickness (≈30∙10-4cm),

u is the superficial velocity of the liquid (≈0.01-0.2cm/s) and D is the

dispersion coefficient of the liquid (1-5∙10-5cm2/s). In our case it was found

that the axial dispersion model can be used as shown in Figure 4.5.

Figure 4.5 Flow model selection based on fluid properties, flow conditions and vessel geometry [8].

Furthermore, it should be noted that this RTD study was based on the

assumption that the inlet signal of the tracer is a very sharp step and hence

no convolution of the inlet data was needed. This assumption enables a

quicker and simpler data analysis and in the same time it was found that

affected only slightly our results. Due to this simplification, the dispersion

factor would be slightly smaller in reality than the one calculated from the


Page 112

experiment. So this assumption results to the worst case scenario. However,

it should be noted that the step-change in liquid concentration was

monitored in the inlet of the capillary as well in order to define the time zero,

the time when the tracer was reaching the inlet sensor.

Validation of the analysis methodology followed for the RTD experiments

was conducted by performing single-phase experiments with only liquid

flowing along the reactor. The volumetric flowrate of the liquid was set in

the inlet (via the pump) and hence the liquid residence time was calculated

based on (4.1).

𝜏 =

𝑉

𝜐 (4.1)

The calculated residence time of the liquid was then compared with the

experimentally measured one. This was repeated for a range of liquid

flowrates and it was found that in all cases the deviation between the

calculated and the experimental residence time of the liquid was always less

than 5%, confirming the validity of this methodology.

4.3 Results

4.3.1 Flow Patterns

Flow observation of gas-liquid flow systems was conducted by means of a

microscope camera in a PFA circular capillary of 1mm inner diameter. Firstly

the effect of the fluid properties on the observed flow pattern was studied by

observing two different gas-liquid systems, N2/DI water and N2/methanol.

Water and methanol present different surface tension and viscosity as shown

in Table 4-1. It should be also noted that PFA is highly wetted to methanol

while only marginally wetted to water. Moreover, these two flow systems

were studied at various gas-to-liquid ratios in order to investigate the effect

of the gas-to-liquid ratio on the flow pattern. However, the amount of data

collected was not enough to form a flow regime map.


Page 113

In Figure 4.6 the observed flow patterns of the N2/DI water system are

presented for two gas-to-liquid ratios, 0.4 and 40 respectively.

Figure 4.6 Observed flow patterns of the N2/DI water system at different gas-to-liquid ratios (υg=0.2ml/min, υℓ=0.5ml/min on the left and υg=0.2ml/min,


When increasing the gas-to-liquid ratio, the flow pattern gradually changes

from slug flow to slug-annular flow as these are defined in Chapter 2.3.1.

More specifically, when the liquid flowrate decreases, while the gas flowrate

remains constant, the liquid slug length decreases and the gas bubble length

increases significantly.

In Figure 4.7 the observed flow patterns of the N2/methanol system are

presented for two gas-to-liquid ratios, 0.4 and 40 respectively. Slug-annular

was the observed flow pattern in both cases with thin liquid slugs and very

long gas bubbles.

Figure 4.7 Observed flow pattern of the N2/methanol system at different gas-to-liquid ratios (υg=0.2ml/min, υℓ=0.5ml/min on the left and υg=0.2ml/min,


It was observed that as the gas-to-liquid ratio increases (by decreasing only

the liquid flowrate), there is no flow pattern change even for a 100 times

change in the gas-to-liquid ratio. However, as the gas-to-liquid ratio

increases, the liquid slugs become thinner and less frequent. Flow patterns

such as churn or annular flow were not observed in the range of velocities


Page 114

used in this study as significantly larger gas velocities are required for the

formation of these inertia-dominated flow regimes [93].

At high gas-to-liquid ratios, the N2/methanol system showed much larger

gas bubbles compared to the N2/water system. This is due to the increased

contact angle of water on the PFA surface that prevents the further spreading

of the liquid on the wall and leads to the formation of frequent, short slugs,

which was also observed by Barajas [73].

Furthermore, it was observed that the transition from slug flow to slug-

annular flow moved to lower gas-to-liquid ratios (lower liquid superficial

velocity when keeping constant gas superficial velocity) with decreasing

surface tension ( 0.0221 /methanol N m < 0.072 /water N m ), in agreement with

previous hydrodynamic studies in microchannels [82,96,179-181].

Hence, in the N2/water system slug flow was observed for smaller gas-to-

liquid ratios than in the N2/methanol system, which is expected as when the

surface tension of the system is large, the system in an attempt to minimise

the energy, lowers the interfacial area between the gas and the liquid. In

other words, earlier transition from slug to slug-annular is observed in

decreasing surface tension as liquid is easier to break through in this case.

4.3.2 Residence Time Distribution Experiments

4.3.2.1 Effect of Gas-to-Liquid Ratio on Dispersion Number

In order to study the effect of gas-to liquid ratio on the RTD and the

dispersion of the liquid, RTD experiments of a N2/water system were

performed at different gas-to-liquid ratios in circular PFA capillary of 1mm.

The gas-to-liquid ratio was adjusted by increasing the liquid flowrate while

keeping the gas flowrate constant. The F(t) curve in Figure 4.8 represents the

normalised data of the original signal of the step-change in liquid

concentration as recorded by the IR sensor in the outlet of the capillary. It

should be noted that the F(t) curve in Figure 4.8 is plotted against the


Page 115

normalised time for each experiment, using as basis the residence time of

each experiment.

Figure 4.8 Experimental F curves for different liquid flowrates (vl) at constant gas flowrate (υg=0.2ml/min) for a N2/water system in a circular PFA capillary of 1mm

inner diameter.

In Figure 4.8, as the gas-to-liquid flowrate ratio decreases the curves become

steeper indicating that the flow approaches plug flow behaviour. The

dispersion number was calculated for each curved based on (4.2) [8],

𝑑𝑖𝑠𝑝𝑒𝑟𝑠𝑖𝑜𝑛 𝑛𝑢𝑚𝑏𝑒𝑟 = (

𝐷

𝑗ℓ𝐿)

(4.2)

Where D is the dispersion coefficient, jℓ the superficial liquid velocity and L

is the channel length. The flow can be considered plug when the dispersion

number is smaller than 0.01 [8]. In the case of the N2/water system,

dispersion number found to be smaller than 0.01 for gas-to-liquid ratios

smaller than 5. When the dispersion number is larger than 0.01, in the case of

N2/water for gas-to-liquid ratios above 5, axial dispersion becomes

noticeable.


Page 116

In Figure 4.9 the dispersion number of the system is shown as a function of

the liquid flowrate (while the gas flowrate was kept constant) and as a

function of the gas-to-liquid ratio.

Figure 4.9 Dispersion number for different liquid flowrates at 0.2ml/min gas flowrate for a N2/water system in a circular PFA capillary of 1mm inner diameter.

The dispersion number increases sharply when decreasing the liquid

flowrate, hence increasing the gas-to-liquid ratio. This could be explained by

the fact that when the gas-to-liquid ratio is very large, the liquid slugs are

very short and are followed by very long gas bubbles. This is leading to

incomplete mass-exchange with the stagnant liquid film causing excessive

broadening of the step change.

This behaviour has been observed also by Kreutzer et al. [182] who studied

the effect of segmentation on dispersion in microchannels. They observed

that dispersion is small when gas-to-liquid ratio is small, although their

range of gas-to-liquid ratios was smaller, ranging between 0.1-2.1.

In this study the range of gas-to-liquid ratios was much wider ranging

between 0.4-40 and it was observed that the dispersion number of the

N2/water system becomes significant (D/𝑗ℓL>0.01) for gas-to-liquid ratios


Page 117

above 5, above which the flow starts deviating from the ideal plug flow

behaviour.

Similar behaviour has been also reported in larger systems, when studying

the hydrodynamic performance of gas-liquid systems related to residence

time distribution in static mixers with inner diameter around 4cm [183].

They reported larger dispersion numbers when decreasing the liquid-side

Reynolds number at constant gas-side Reynolds number. They attributed

this behaviour to the lower liquid holdup at smaller liquid-side Reynolds

numbers resulting in large dispersion numbers. At high gas velocities a

competitive phenomenon it taking place as the average liquid velocities will

increase resulting to smaller dispersion numbers.

4.3.2.2 Effect of Fluid Properties on Dispersion Number

To study the effect of fluid properties on the dispersion, residence time

distribution experiments were performed using two different fluids, DI

water and a 10% aqueous solution of glycerol together with nitrogen in both

cases. These fluids were chosen as they have similar surface tensions but

different viscosities (Table 4-1).

The RTD curves of the two systems are shown in Figure 4.10. In both cases

the liquid flowrate was equal to 0.3ml/min while the gas flowrate was set at

0.2ml/min and the capillary used for this study was made of PFA and its

inner diameter was 1mm. It is clear that the N2/glycerol system presents a

steeper F-curve indicating a more plug flow behaviour than the N2/water

system. This is due to the increased viscosity of glycerol, as when nitrogen

breaks through the glycerol slug (more viscous than water), more driving

force is needed. Hence a thicker film of glycerol is formed around the

nitrogen bubble compared to the N2/water system at same velocities which

results a lower dispersion number for the system. In other words, due to the

increased viscosity, the capillary number of the system increases (Ca=0.079

for N2/water system and Ca=0.105 for N2/glycerol system), hence the film


Page 118

thickness of the gas-liquid system increases [174,184] which leads to a

smaller dispersion number for the system [185].

Figure 4.10 Experimental F curves for N2/water (green line) and N2/10% aqueous glycerol (blue line) at 0.3ml/min liquid flowrate and 0.2ml/min gas flowrate in a

circular PFA capillary of 1mm inner diameter.

This behaviour is in agreement with previous observations of Zhang et al.

[179] who studied the effect of physical properties on gas-liquid

hydrodynamics in glass microchannels with inner diameters ranging

between 302-916µm. They found that the liquid film around the bubbles

becomes thicker by increasing the fluid’s viscosity or by decreasing its

surface tension leading to less dispersion in the system.

Figure 4.11 shows the effect of liquid flowrate on the dispersion number for

the two systems of different viscosity when keeping the gas flowrate

constant. Glycerol shows smaller dispersion numbers for every liquid

flowrate due to its larger viscosity compared to water that causes thicker

films around the gas bubbles. This difference on dispersion numbers

between the two fluids becomes bolder for smaller liquid flowrates, hence at

large gas-to-liquid ratios. This is because at large gas-to-liquid flowrates the

flow pattern moves to a more annulus-type flow pattern where the film


Page 119

thickness becomes a more critical parameter for mass transfer in the

capillary. On the contrary, as the gas-to-liquid ratio decreases (i.e. as the

liquid flowrate increases in Figure 4.11) and moves to a more slug-type flow,

the effect of viscosity gradually fades away.

Figure 4.11 Dispersion number against liquid flowrate for N2/water (blue line) and N2/10% aqueous glycerol (red line) at 0.2ml/min gas flowrate in a PFA circular

capillary of 1mm inner diameter.

4.3.2.3 Effect of Channel Size on Dispersion Number

The effect of the capillary diameter on the dispersion was studied by

performing RTD experiments with a N2/water system in capillaries of

different inner diameters (Figure 4.12). Three capillary diameters were tested

varying from 0.25, 0.5 and 1mm. The liquid and gas flowrates were kept

constant in all cases at 0.1 and 0.2ml/min respectively.

Increasing the tube diameter, F curves become steeper, hence less dispersion

is observed and the flow approaches a more plug flow type behaviour. This

is because in larger tubes the velocities are smaller resulting to lower

Reynolds numbers. And lower Reynolds numbers lead to decrease of the

film thickness in slug-annular flow and consequently decrease of the

dispersion in the system.


Page 120

Figure 4.12 Experimental F curves of a N2/water system in PFA circular capillaries of different inner diameters at 0.2ml/min gas flowrate and 0.1ml/min liquid flowrate.

4.3.2.4 Effect of Channel Size on Void Fraction

The effect of capillary diameter on void fraction was tested by performing

RTD experiments for a N2/water system in circular capillaries with inner

diameters of 0.25, 0.5 and 1mm. The liquid flowrate was varied between

0.005-0.5ml/min while the gas flowrate was kept constant at 0.2ml/min. The

void fraction of the system was estimated based on equation (4.3).

휀𝑔 = 1 −𝜏ℓ ∙ 𝜐ℓ

𝑉𝑡𝑜𝑡𝑎𝑙 (4.3)

where 𝜏ℓ is the liquid mean residence time calculated from the RTD

experiments, 𝜐ℓ is the liquid volumetric flowrate and 𝑉𝑡𝑜𝑡𝑎𝑙 is the reactor’s

volume.

Figure 4.13 shows the void fraction results for the different circular

capillaries. The void fraction is plotted against a homogenous void fraction

(𝛽 = 𝑗𝑔 𝑗𝑔 + 𝑗ℓ)⁄ with different symbols used for the different capillaries.


Page 121

Figure 4.13 Void fraction of N2/water against volumetric quality at 0.2ml/min gas flowrate in circular PFA capillaries of 0.25, 0.5 and 1mm inner diameter.

It is clear that the void fraction is not strongly dependent on the diameter of

the capillary.

The bold line in the figure represents homogenous model (휀𝑔 = 𝛽 ) while the

dashed curve corresponds to Armand’s model [108] (휀𝑔 = 0.833 ∙ 𝛽). Both

homogenous and Armand’s model provide linear relation for the void

fraction. The void fraction in the present system seems to be well described

by homogenous model for high volumetric qualities (β>0.65). As the

volumetric quality decreases below 0.7, the void fraction deviates largely

from homogenous model and can be better predicted by Armand’s model.

This behaviour can be explained by assuming that flow pattern changes from

annular to slug flow (for β<0.65). Armand’s model though is only applicable

in a small range of volumetric qualities (0.65>β>0.45) [108]. Comparison with

more hydrodynamic models available in the literature was performed but

overall, no previous hydrodynamic model can describe our experimental

data in the whole operating range (see Appendix, Figure A. 30).

For this reason, a new correlation was developed to fit the void fraction

behaviour of a N2/water system in the whole range of volumetric qualities in


Page 122

circular capillaries of 0.25-1mm inner diameter. The correlation as shown in

(4.4) is only a function of the volumetric quality, β.

(4.4)

In Figure 4.14 the void fraction predictions of the suggested correlation is

plotted together with the experimental data of the N2/water system.

Figure 4.14 Fit of proposed correlation for the void fraction of N2/water systems in circular PFA capillaries with inner diameter 0.25-1mm.

The proposed correlation can fit the full set of the experimental void fraction

data with great accuracy. This indicates that this correlation (4.4) can be used

with confidence to predict the void fraction of a N2/water system in circular

capillaries with inner diameter 0.25-1mm.

4.3.2.5 Effect of Fluid Properties on Void Fraction

The effect of fluid properties on void fraction was investigated by

performing a series of RTD experiments with three different gas-liquid

systems, N2/water and N2/methanol and N2/10% glycerol (in water). The

liquid flowrate was varied between 0.005-0.8ml/min while the gas flowrate

2.11

2.11

2

1G


Page 123

was kept constant at 0.2ml/min. A circular PFA capillary was used in all

experiments with 1mm inner diameter.

Figure 4.15 shows the void fraction results for the two different systems. The

void fraction is plotted against liquid volumetric flowrate with different

symbols used for the different gas-liquid systems.

Figure 4.15 Void fraction of N2/water (blue line), N2/glycerol (green line) and N2/methanol (orange line) against liquid flowrate at 0.2ml/min gas flowrate in a

circular PFA capillary of 1mm.

At very large void fractions (or very small liquid flowrates) the nature of the

liquid does not seem to affect the void fraction of the system significantly.

This is because the volume of liquid in the system in this case is very small

and hence its effect is insignificant. However, when increasing the liquid

flowrate (or decreasing the void fraction), the dependence of the fluid’s

nature on the void fraction becomes larger. Specifically, for a certain liquid

flowrate, the void fraction of the N2/methanol system is larger than the void

fraction of the N2/glycerol system which in turn is larger than the void

fraction of the N2/water system. The surface tension of methanol is much

smaller of glycerol and water (𝛾𝑀𝑒𝑡ℎ𝑎𝑛𝑜𝑙 =0.0221N/m, 𝛾𝐺𝑙𝑦𝑐𝑒𝑟𝑜𝑙 =0.0705N/m,

𝛾𝑊𝑎𝑡𝑒𝑟 =0.072N/m). Hence, it appears that the lower the surface tension of


Page 124

the fluid, the larger the void fraction of the system will be for certain gas and

liquid velocities. This can be explained by the fact that when the surface

tension of a system decreases, the dispersion number of the system decreases

as well (as we observed earlier in Chapter 4.3.2.2). This effect becomes bolder

at higher liquid flowrates (smaller void fractions) due to the increased

amount of liquid in that case.

4.4 Conclusions

Hydrodynamic study of gas-liquid systems was performed experimentally

in circular microcapillaries at very small gas and liquid superficial velocities.

The capillaries were made of PFA and their diameter ranged between 0.25-

1mm. Gas and liquid superficial velocities were varied between 0.004-

0.068m/s and 0.0001-0.102m/s respectively. Hydrodynamic characteristics

such as the flow pattern, the void fraction and the residence time distribution

were experimentally measured and their dependence on the fluid properties,

the capillary diameter and the gas-to-liquid ratio was investigated.

For this purpose flow observation of N2/methanol and N2/water was

performed at a range of gas-to-liqiud ratios (jg:jℓ=0.66-40) in a circular PFA

capillaries of 1mm inner diameter. It was found that at high gas-to-liquid

ratios, the N2/methanol system showed much larger gas bubbles compared

to the N2/water system. This was due to the increased contact angle of water

on the PFA surface that prevented the further spreading of the liquid on the

wall and led to the formation of frequent, short slugs, phenomenon which

was also observed by Barajas [73]. Furthermore, it was observed that the

transition from slug flow to slug-annular flow moved to lower gas-to-liquid

ratios with decreasing surface tension, in agreement with previous studies

[82,96,179-181].

Moreover, residence time distribution measurements of various gas-liquid

systems such as N2/methanol, N2/water and N2/ 10% glycerol (in water)

were conducted at a range of gas-to liquid ratios (jg:jℓ=0.66-40) in circular


Page 125

PFA capillaries with various inner diameters. It was found that as the gas-to-

liquid flowrate ratio increases, axial dispersion in the system increases,

behaviour also reported by Kreutzer et al. [182]. This was explained by the

fact that when the gas-to-liquid ratio is very large, the liquid slugs are very

short and followed by very long gas bubbles. This is leading to incomplete

mass-exchange with the stagnant liquid film causing excessive broadening of

the step change. In the case of the N2/water system, it was found that axial

dispersion becomes noticeable for gas-to-liquid ratios above 5.

Moreover, when increasing the viscosity of the liquid, less axial dispersion

was observed in the system, behaviour also reported by Zhang et al. [179].

This was explained by the thicker film that was formed around the bubble,

as the driving force of the gas to break through a more viscous liquid was

larger leading to a smaller dispersion number [174,184,185]. This difference

on dispersion numbers between two fluids with different viscosities found to

become larger for smaller liquid flowrates, hence at large gas-to-liquid ratios.

This is because at large gas-to-liquid flowrates the flow pattern moves to a

more annulus-type flow pattern where the film thickness becomes a more

critical parameter for mass transfer in the capillary. On the contrary, as the

gas-to-liquid ratio decreases (i.e. as the liquid flowrate increases in Figure

4.11) and moves to a more slug-type flow, the effect of viscosity gradually

fades away.

Furthermore, it was found that by increasing the tube diameter, less

dispersion is observed in the system and the flow approaches a more plug

flow type behaviour. This is because for the same gas and liquid flowrates,

the superficial velocities are smaller in capillaries with larger diameters

resulting to smaller Reynolds and capillary numbers leading to smaller

dispersion numbers [183,185].

Moreover, experimental data of void fraction of a N2/water system in

capillaries with various inner diameters (0.25-1mm) in a range of gas-to


Page 126

liquid ratios (0.3-400) showed that the void fraction is not strongly

dependent on the inner diameter of the capillary in this range of diameters.

The void fraction data of this system were well described by homogenous

model at high volumetric qualities (β>0.65) and by Armand model for

moderate volumetric qualities (0.65>β>0.45). As the volumetric quality

decreased below 0.45, the void fraction deviated largely from both models

and no other hydrodynamic model was well predictive either. For this

purpose, a new correlation was developed which found to fit the full set of

void fraction data with great accuracy.

Finally, it was observed that the nature of the liquid affect the void fraction

only in very small gas-to-liquid ratios, when the amount of liquid in the

system is hence not very small. It was found that the lower the surface

tension of the liquid, the larger the void fraction of the system will be for

certain gas and liquid velocities, due to the increased dispersion number in

that case.

Page 127

CHAPTER 5. Methoxycarbonylation of Ethylene: Set-up

Design and Preliminary Experiments

5.1 Introduction

In this chapter the design of the set-up for the kinetic study of

methoxycarbonylation of ethylene is presented. The set-up can withstand

elevated temperature and pressure conditions required for this reaction

system and safety precautions are taken due to the poisonous nature of the

reactants. The design of the reactor is discussed focusing on the material’s

choice, its permeability, reactivity and isothermality.

Residence time distribution studies were performed in order to determine

the hydrodynamic characteristics of the system such as the void fraction and

the residence time distribution under reaction conditions.

A reactor model was developed to describe the phenomena of reaction and

mass transfer in the capillary reactor. Due to the high pressure of the system

it was not feasible to collect experimental data directly at the inlet and outlet

of the reactor. Instead experimental data for the outlet side for example were

collected downstream after the gas and liquid were separated at ambient

pressure and temperature conditions. A vapour-liquid equilibrium model

was used to convert the experimental data to the conditions in the inlet and

outlet of the reactor.

Blank experiments without catalyst in the feed and experiments at standard

operating conditions were performed to validate the accuracy of the analysis

methods and the system for an accurate kinetic study.

CHAPTER 5. Methoxycarbonylation of Ethylene: Set-up Design and Preliminary Experiments

Page 128

5.2 Experimental Set-Up Design for Kinetic Experiments

A flow set-up (Figure 5.1) that can withstand elevated temperature and

pressure conditions (up to 12bara and 120oC) was built for the kinetic study

of methoxycarbonylation of ethylene by a homogenous Palladium based

catalyst.

Figure 5.1 Schematic of the flow set-up for the kinetic study of methoxycarbonylation of ethylene at elevated temperature and pressure conditions.

The gases were controlled by three mass flow controllers (up to

1ml25oC,1bar/min for CO, up to 3ml25oC,1bar/min for C2H4 and He) that can

operate at pressures up to 12bar. Upstream of each mass flow controller

particle microfilters were installed to prevent any particles from the

cylinders to enter the set-up. In addition, downstream of each mass flow

controller check valves were installed to prevent any liquid backflush. The

mass flow controllers were calibrated by means of a bubble meter and

equation (3.16) and their calibration line can be found in the Appendix

(Figure A. 4-Figure A. 6).

A catalytic liquid mixture was prepared on site by diluting a 99:1 v/v

MeP:MeOH catalytic solution (provided by Lucite International) with

methanol and methyl propionate to the desired concentration. The final

catalytic mixture contained 5.86ppm Palladium and had a molar ratio of


Page 129

1:5:450 in Pd:Alpha ligand:Methanesulfonic acid. The mixture was prepared

in a glove box under argon atmosphere to prevent catalyst deactivation by

oxygen poisoning (Appendix J). Then, the liquid was added in a stainless

steel syringe of 8ml and was delivered to the reactor after passing a liquid

filter for particles above 10μm.

The liquid stream was added to the ethylene stream via a T-junction and

flowed through a pre-treatment section at 100oC. The pre-treatment section

consisted of a 2m long Hastelloy capillary with 1.75mm inner diameter and

1/8in outer diameter. After the pre-treatment section, carbon monoxide was

introduced to the system via a T-junction and the gas-liquid mixture entered

the reactor at 100oC where the reaction begun. The pressure was always kept

constant at 10bara via a back pressure regulator.

The reactor was a 6m long Hastelloy capillary with 1mm inner diameter and

1/16in outer diameter. The reactor was tested for its isothermality and

permeability as well as its surface reactivity (Appendix J). It was concluded

that no fluoropolymer tubing (i.e. PFA, ETFE, PEEK, Halar, ECTFE) was

suitable for the kinetic study of the MeP system as they are permeable to

ethylene at elevated temperature. Hastelloy however found to be suitable for

this kinetic study, as it is not permeable to any of the reactants even at

elevated temperature and it provides an inert and hence non-reactive

internal surface.

Both capillaries for pre-treatment and reaction were placed in an oil bath

with a stirrer on a hot plate to control the temperature.

After the reactor the gas-liquid mixture entered a gravity-based separator

made of stainless steel. The liquid exited from the bottom of the separator,

where a metering valve helped to achieve a more controlled and smooth

liquid sampling without sudden pressure drops. The gas exited from the top

of the separator and passed through the back pressure regulator (BPR,

Brooks 5866) that maintained the pressure of the system at the desired value.


Page 130

The gas exiting the separator was analysed online using gas chromatography

(GC). A liquid trap was placed before the GC in order to prevent any liquid

entering the GC. The gas flowrate in the outlet was measured by a bubble

meter. More details on the analysis methodology and calibration can be

found in the Appendix J. Reproducibility of the gas phase analysis found

equal to 0.5%, while for the liquid phase analysis equal to 2%.

The pressure of the system was monitored by means of a pressure

transducer installed at the inlet of the reactor. The calibration of the pressure

transducer can be found in the Appendix (Figure A. 7). The set-up was

regularly checked for leaks by pressurising the set-up at 12bar with helium

in order to ensure that the system is not leaking.

The standard operating procedure employed for the experiments can be

found in the Appendix (Appendix J).

Blank experiments without catalyst in the feed and experiments at standard

operating conditions were performed (Appendix J). The carbon balance

closed within 3% difference, validating the accuracy of the analysis methods

and the system for an accurate kinetic study.

5.3 Residence Time Distribution Studies under Reaction

Conditions

Residence time distribution (RTD) studies of the gas-liquid system were

conducted under reaction conditions. Based on residence time distribution

experiments, information for the mean residence time of the liquid, the void

fraction and the mixing quality of the system were collected under reaction

conditions. In this way, effects such as changes in the flow behaviour along

the reactor due to reaction (e.g decrease of gas flowrate) or flow anomalies

along the reactor (e.g waves) were taken into account, which would be


Page 131

impossible to do if studying the hydrodynamics of the system under non-

reactive conditions or if using relative hydrodynamic correlations.

Residence time distribution (RTD) experiments were performed by means of

two optical (IR) sensors (Chapter 4.2) that were installed just before and after

the reactor. A step-change of the liquid feed concentration was introduced to

the reactor by a 6-port valve (that was installed just after the syringe pump)

and the change of this step-change was monitored by the two optical sensors

in the inlet and the outlet of the reactor. More information about the

methodology followed and the underlying theory can be found in Chapter

4.2.1 where the same methods were used for the hydrodynamic analysis of a

much simpler, non-reactive gas-liquid system.

For the step-change of the liquid feed concentration methanol was used as

the tracer which will not disturb the system as it is already present as one of

the reactants in the system. The effect of the tracer on the RTD results has

been studied further and the results can be found in Appendix J.

RTD experiments were conducted under different gas to liquid ratios. Gas to

liquid ratios ranged from 23 to 222. The reactor design and operating

conditions are the same as previously. The purpose of these experiments was

to investigate the hydrodynamics of the MeP system in order to decide the

conditions for the kinetic study. The main criteria were the gas-liquid system

to present plug flow behaviour, no mass transfer resistances and liquid

residence time enough for accurate measurement of reaction performance.

Four different sets of gas, liquid flowrates and gas-liquid ratios were tested

(Table 5-1).


Page 132

Table 5-1 Gas and liquid flowrates at reactor’s conditions (100oC, 10bara) for the different cases tested.

Case A B C D

υg (ml/min) 0.178 0.277 0.271 0.182

υℓ (ml/min) 0.0077 0.0083 0.00144 0.00082

g/ℓ ratio 23 33 188 222

Flow pattern Slug-

annular

Slug-

annular Annular Annular

Liquid slug length (mm) <2 <2 - -

Bubble length (cm) 20 30 600 600

For case A, the observed flow pattern was slug-annular with Lbubble>20cm

and Lslug<2mm. The flow for case B was slug-annular with elongated bubbles

(Lbubble>30cm) and relatively short liquid slugs (Lslug<2mm), while for cases

C and D, the observed flow pattern was pure annular flow with no

appearance of liquid slugs. It should be noted that the flow observation was

performed at 25oC and that at reaction conditions (100oC) it is expected the

flow to be closer to annular flow in all cases. The results of the RTD

experiments for cases A-D are shown in Table 5-2.

Table 5-2 Results of RTD experiments for different gas-liquid ratios.

Case

Gas-

liquid

ratio

Mean

liquid

residence

time, τℓ

(min)

Dispersion

factor,

D/uL

Void

fraction,

ε

Film

Thickness

(µm)

Void

fraction

prefactor,

A

A 23 45.2 0.003 0.926 19 0.949

B 33 30.5 0.006 0.946 14 0.956

C 188 63.9 0.023 0.98 5 0.979

D 222 89 0.026 0.984 4 0.985


Page 133

Liquid residence time (reaction time) up to ca. 90min was obtained with the

current reactor design, enough for accurate reaction performance

measurements during the kinetic study. For cases A and B the flow satisfied

the plug flow criterion (D/uL<0.01) while for cases C and D the flow

deviated from plug flow behaviour.

The void fraction, ε, found to increase as the gas-to-liquid ratio increases,

due to the increase of the gas volume and/or decrease of liquid volume. The

liquid film thickness was calculated for each case based on the RTD results

and found to decrease as the gas-to-liquid ratio increases. This is because as

the gas-to-liquid ratio increases, the gas moves faster (in comparison with

the liquid), pushing the liquid towards the walls, creating a thinner liquid

film around the bubbles. Moreover, it is worth noting that the void fraction

prefactor, A, does not remain constant as the gas-to-liquid ratio increases but

increases. Specifically, as the gas-to-liquid ratio increases, the void fraction

prefactor approaches the homogenous model prediction.

It was concluded that the flowrates of case A are the most suitable for the

kinetic study as it fulfils all the criteria and is the quicker one.

5.5 Analysis Methodology and Reactor Model

In Figure 5.2 a simplified schematic of the experimental set-up for the kinetic

experiments is shown that highlights where the composition of the gas and

liquid streams change either because of a temperature change (resulting to a

new vapour-liquid equilibrium) or because of reaction.

For the kinetic study, the gas and liquid composition and the flowrates are

required at the inlet and outlet of the reactor (point 1 and 2 in Figure 5.2).

However, in our flow set-up it was not feasible to analyse the gas and liquid

streams directly at these points due to the elevated pressure. Instead,

experimental data were collected in the feed of the set-up (point 0 in Figure

5.2) and in the outlets of the gas and the liquid (point 4 and point 5 in Figure


Page 134

5.2), based on which the conditions in the separator (point 3 in Figure 5.2)

were determined.

Figure 5.2 Simplified schematic of the experimental set-up for kinetic experiments demonstrating the main points where gas and liquid composition changes either

because of temperature change (new VLE) or because of reaction.

In order to estimate the compositions of the gas and liquid streams in the

inlet and outlet of the reactor (at point 1 and 2) based on experimental data at

point 0 and 3 a vapour-liquid equilibrium (VLE) model was used as new

VLE was established due to the different temperature conditions between

these points. More details on the VLE model can be found in the Appendix J.

The reactor model previously developed and validated with a model system

(carbon dioxide absorption in buffer solutions-Chapter 3), is now applied for

the MeP system to be able to describe the change of the molar flowrates of all

components (CO, C2H4, MeOH, MeP) in both gas and liquid phases along

the reactor. The reactor model was based on (5.1) and (5.2) which were

solved using gPROMS.

1

𝐴𝑐

𝑑𝐹𝑖ℓ

𝑑𝑥= 𝑣𝑖 ∙ 𝑟𝑥𝑛(𝑧) ∙ 휀ℓ + 𝑘ℓ𝛼 ∙ (

𝐶𝑖𝑔

𝐾𝑖− 𝐶𝑖

ℓ)

(5.1)

1

g g

i ii

c i

dF Ck C

A dx K

(5.2)


Page 135

where, iC and g

iC and iF and g

iF are the concentrations (mol/ml) and the

molar flowrates (mol/min) of component i (MeOH, MeP, CO, C2H4) in the

liquid and in the gas phase respectively, x is the axial coordinate, cA is the

cross sectional area (cm2), 𝑣𝑖 is the reaction stoichiometric coefficient (equal

with -1 for the reactants and with 1 for the products), ( )rxn z is the reaction

rate (mol/ml min), is the liquid volume fraction of the system, k is the

mass transfer coefficient (min-1) of the system and iK is the gas-liquid

equilibrium constant. The actual reactor model in gPROMS is given in

Appendix E. The boundary conditions for (5.1) and (5.2) were the known

molar flowrates of all components in the inlet of the reactor (point 1, Figure

5.2) calculated by means of the VLE model and the experimental results in

the inlet of the set-up (point 0, Figure 5.2).

The liquid side volumetric mass transfer coefficient k was estimated by

van Baten and Krishna [105] model shown in (5.3).

(5.3)

The system found to be under kinetic control (Appendix J). It is worth noting

that as the reaction is very slow, the value of the mass transfer coefficient

does not affect the results.

The value of was determined by residence time distribution experiments.

The value of the equilibrium constant iK was calculated by (5.4) for carbon

monoxide and ethylene and (5.5) for methanol and methyl propionate by

means of the VLE model at the inlet conditions of the reactor.

𝐾𝑖 =

𝛾𝑖 ∙ 𝐻𝑒𝑖 ∙ 𝜐ℓ

𝐹𝑖ℓ ∙ 𝑅 ∙ 𝑇

(5.4)

𝐾𝑖 =

𝛾𝑖 ∙ 𝑃𝑖𝑣𝑎𝑝 ∙ 𝜐ℓ

𝐹𝑖ℓ ∙ 𝑅 ∙ 𝑇

(5.5)

, ,

42 42 3.41

gBcap cap film film

UC film

Du Dk k k

d L d


Page 136

where iis the activity coefficient (-),

iHe is the Henry’s constant (bar), vap

iP is

the vapour pressure (bar) of component i, is the total liquid volumetric

flowrate (ml/min) and tF is the total molar flowrate (mol/min) of the liquid

phase. It was assumed that iK remains constant along the reactor, as the

liquid volumetric flowrate, the temperature and the pressure of the system

did not change significantly along the reactor.

5.6 Conclusions

The design of a high-pressure set-up for the kinetic study of

methoxycarbonylation of ethylene was discussed in detail. Methods for the

analysis of gas and liquid phase by gas chromatography were developed and

validated. The design of the reactor was discussed focusing on the material’s

choice, its permeability, reactivity and isothermality.

Residence time distribution (RTD) studies were performed at different gas-

to-liquid ratios under reaction conditions to determine the residence time of

the liquid, the void fraction and the mixing quality of the system under

reaction. Liquid residence time (reaction time) up to ca. 90min was obtained

with the current reactor design, enough for accurate reaction performance

measurements during the kinetic study. The flow found to satisfy the plug

flow criterion for gas-to-liquid ratios below 33 while for larger ratios the flow

deviated from lug flow behaviour.

The void fraction of the system found to increase as the gas-to-liquid ratio

increased, due to the increase of the gas volume and/or decrease of liquid

volume. The liquid film also decreased as the gas-to-liquid ratio increased.

Moreover, the void fraction prefactor did not remain constant as the gas-to-

liquid ratio increases but increased. It was concluded that a gas-to-liquid

ratio of 23 is the most suitable for the kinetic study as it provides enough

residence time for the reaction and results to plug flow behaviour.


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The reactor model that will be applied to describe the phenomena of reaction

and mass transfer in the capillary reactor in this kinetic study was presented.

A vapour-liquid equilibrium model will be used to convert the experimental

data to the conditions in the inlet and the outlet of the reactor.

Page 138

CHAPTER 6. Kinetic Study of Methoxycarbonylation

of Ethylene: Experiments and Modelling

6.1 Introduction

In this chapter, the kinetic study of methoxycarbonylation of ethylene is

presented in a flow system. The main aim is the development of a rate

expression that describes accurately the effect of methanol, ethylene and

carbon monoxide concentration and of temperature over a wide range of

conditions. Experiments are performed in a Hastelloy capillary microreactor

of 1mm inner diameter and 6m length. The experimental conditions include

a temperature range of 80-120oC, gas inlet molar ratio ethylene-to-carbon

monoxide range of 1.25-10 and a liquid inlet concentration range of 22-90%

wt. methanol-to-methyl propionate while pressure is kept constant at 10bara.

The catalyst used in this study is the homogeneous [Pd(dtbpx)(dba)]

(dba=trans, trans-(PhCH=CH)2CO) that was developed by Lucite

International is capable of converting ethylene, carbon monoxide and

methanol to methyl propionate at a rate of 50000 mol of product per mol of

catalyst per hour with a selectivity of 99.98% [132,134].

A mechanistic kinetic model that can describe satisfactorily the system’s

behaviour is developed based on the Palladium hydride catalytic cycle.

Parameter estimation of the kinetic model is performed in order to achieve

good fit of the experimental data. The accuracy of the estimation is evaluated

using statistical tools. Information analysis is also performed to evaluate how

informative the experimental data were for the model parameters estimation.

CHAPTER 6. Kinetic Study of Methoxycarbonylation of Ethylene: Experiments and Modelling

Page 139

6.2 Experimental

6.2.1 Experimental Set-up

A series of kinetic experiments of methoxycarbonylation of ethylene were

performed in a flow set-up in order to study. The purpose of these

experiments was to study the effect of various parameters, such as the

reactants concentration and temperature effect on the kinetics of the system.

The flow set-up used for these experiments is shown in Figure 6.1 and can

withstand elevated temperature and pressure conditions (up to 12bara and

120oC). The gases were controlled by three mass flow controllers (up to

1ml25oC,1bar/min for CO, up to 3ml25oC,1bar/min for C2H4 and He) that can

operate at pressures up to 12bar. Upstream of each mass flow controller

particle microfilters were installed to prevent any particles from the

cylinders to enter the set-up. In addition, downstream of each mass flow

controller check valves were installed to prevent any liquid backflush. The

mass flow controllers were calibrated by means of a bubble meter and

equation (3.16) and their calibration line can be found in the Appendix

(Figure A. 4-Figure A. 6).

Figure 6.1 Schematic of the flow set-up for the kinetic study of methoxycarbonylation of ethylene at elevated temperature and pressure conditions.


Page 140

The liquid feed was added in a stainless steel syringe of 8ml and was

delivered to the reactor after passing a liquid filter for particles above 10μm.

The liquid stream was added to the ethylene stream via a T-junction and

flowed through a pre-treatment section at 100oC. The pre-treatment section

consisted of a 2m long Hastelloy capillary with 1.75mm inner diameter and

1/8in outer diameter. After the pre-treatment section, carbon monoxide was

introduced to the system via a T-junction and the gas-liquid mixture entered

the reactor at 100oC where the reaction begun. The pressure was always kept

constant at 10bara via a back pressure regulator. The reactor was a 6m long

Hastelloy capillary with 1mm inner diameter and 1/16in outer diameter.

Both capillaries for pre-treatment and reaction were placed in an oil bath

with a stirrer on a hot plate to control the temperature.

After the reactor the gas-liquid mixture entered a gravity-based separator

made of stainless steel. The liquid exited from the bottom of the separator,

where a metering valve helped to achieve a more controlled and smooth

liquid sampling without sudden pressure drops. The gas exited from the top

of the separator and passed through the back pressure regulator (BPR,

Brooks 5866) that maintained the pressure of the system at the desired value.

The gas exiting the separator was analysed online using gas chromatography

(GC). A liquid trap was placed before the GC in order to prevent any liquid

entering the GC. The gas flowrate in the outlet was measured by a bubble

meter.

The pressure of the system was monitored by means of a pressure

transducer installed at the inlet of the reactor. The calibration of the pressure

transducer can be found in the Appendix (Figure A. 7).

The set-up was regularly checked for leaks by pressurising the set-up at

12bar with helium in order to ensure that the system is not leaking.


Page 141

The standard operating procedure employed for the experiments can be

found in the Appendix (Appendix E).

6.2.2 Operating Conditions

The kinetic study of methoxycarbonylation of ethylene was performed at

100oC and at 10bara. Gas and liquid flowrates were kept constant in all cases

at 0.1ml25oC,10bara/min and 0.005ml/min respectively. A 99:1 v/v MeP:MeOH

catalytic solution was provided by Lucite International and consists of the

catalyst [Pd(dtbpx)(dba)] (dba=trans, trans-(PhCH=CH)2CO). This catalyst

was developed by Lucite International and is capable of converting ethylene,

carbon monoxide and methanol to methyl propionate at a rate of 50000 mol

of product per mol of catalyst per hour with a selectivity of 99.98% [132,134].

The catalyst solution was then diluted with methanol and methyl propionate

to the desired concentration in %wt. MeP:MeOH. This preparation was

performed in a glove box under Argon atmosphere to avoid any catalyst

deactivation with contact with air. This is because its preparation under air

atmosphere results to deactivation of the catalyst due to the oxygen from the

atmosphere dissolving in the liquid mixture, oxidising and deactivating the

catalyst. For the same reason, the solutions of methanol and methyl

propionate used for the catalyst solution were first degassed with Argon to

remove any dissolved oxygen. The final catalytic mixture contained 5.86ppm

Palladium and had a molar ratio of 1:5:450 in Pd:Alpha

ligand:Methanesulfonic acid. The catalyst concentration was equal to 1.3∙10-3

mol/L in all cases.

6.3 Kinetic Experiments

6.3.1 Dependence of Reaction Rate on Methanol Concentration

In order to study the effect of methanol concentration on the reaction rate

liquid solution concentrations in the feed ranged between 22-90%wt.

MeOH:MeP. Gas concentration in the feed was kept constant at 10%v/v


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CO:C2H4 in all cases. Gas and liquid flowrates were kept constant in all cases

at 0.1ml25oC,10bara/min and 0.005ml/min respectively. The experimental

conditions for the methanol series experiments are shown in Table 6-1.

Table 6-1 Experimental conditions for the methanol series experiments.

Temperature: 100oC

Pressure: 10bara

CO feed partial pressure: 1bara

Ethylene feed partial pressure: 9bara

Liquid feed concentration: 22-90%wt. MeOH: MeP

Pd catalyst concentration: 1.3∙10-3 mol/L

Gas feed volumetric flowrate 0.1ml25oC,10bara/min

Liquid feed volumetric flowrate 0.005ml/min

The results of the methanol series experiments are shown in Figure 6.2.

Figure 6.2 Effect of methanol concentration on turnover frequency for a gas feed stream of 10%v/v CO:C2H4 at 100oC, 10bara.

The observed reaction was measured by means of the turn over frequency

(TOF) which is defined by (6.1),


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𝑇𝑂𝐹 =

𝑚𝑜𝑙 𝑀𝑒𝑃 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑

𝑚𝑜𝑙 𝑃𝑑 𝑖𝑛𝑙𝑒𝑡 ∙ ℎ𝑟 (6.1)

The data are presented as classical log-log plots for methanol concentration

at the outlet of the reactor. It was assumed that there was not significant

change of concentration along the reactor length due to the small

conversions observed. Conversions data for the experiments reported in this

chapter can be found in the Appendix J. The error stated in the graph is

based on the reproducibility of the liquid analysis and corresponds to 95%

confidence.

Although methanol was in excess in these experiments, it has a great effect

on the observed reaction rate. This may indicate that methanol attack of the

ethyl carbonylated complex is not very fast or favoured. In this case a higher

concentration in solution increases the chance of an attack of methanol on the

complex and influences the overall reaction rate in this way. As the

sensitivity to methanol concentration appears high, this probably indicates

that it is the slowest step. This was also observed by Zacchini who carried

out NMR spectroscopic studies for the methoxycarbonylation of ethylene

promoted by the Palladium catalyst, [Pd(dtbpx)(dba)] [136]. This observation

is supported by other researchers as well who studied the

methoxycarbonylation of higher α-olefins [186-188] or the hydroformulation

of alkenes [189,190].

The analysis of these data has been completed by carrying out a regression of

the reaction rate against methanol concentration. The data provided an order

in methanol concentration close to unity. This correlation is only valid

between methanol concentrations of 22-90%wt. MeOH:MeP.

6.3.2 Dependence of Reaction Rate on Ethylene Concentration

For the ethylene series experiments ethylene concentration in the feed

ranged between 23-83%vol. by means of helium acting as the diluting inert


Page 144

gas. Carbon monoxide concentration in the feed was always constant at

10%vol. by means of helium as the diluting gas. The liquid concentration in

the feed was kept constant at 30%wt. MeOH:MeP. The main reason for this

choice of reaction mixture composition is that it has been shown that

decomposition of the catalyst is slower when the level of methanol in the

reaction mixture is low. Gas and liquid flowrates were kept constant in all

cases at 0.1ml25oC,10bara/min and 0.005ml/min respectively. The experimental

conditions are shown in Table 6-2.

Table 6-2 Experimental conditions for the ethylene series experiments.

Temperature: 100oC

Pressure: 10bara


Ethylene feed partial pressure: 2.3-8.3bara

Liquid feed concentration: 30%wt. MeOH: MeP




The results are shown in Figure 6.3 where the lnTOF is plotted against the

concentration of ethylene in the outlet of the reactor. In this range of

operating conditions ethylene appears to have no significant effect on the

reaction rate. The lack of any effect with ethylene concentration is attributed

to its high solubility and the fast mass transfer of the system. Typical

concentration of carbon monoxide in the liquid phase at reaction conditions

are ca. 0.04% while of ethylene ca. 2.4%. Hence, it is expected that the

concentration of ethylene in the solution is not changing very much since it is

always saturated and in excess. Similar behaviour has been also reported by

Seayad [191] who studied the carbonylation of styrene using a homogenous

Pd-complex catalyst and observed zero-order with respect to the styrene.


Page 145

Figure 6.3 Effect of ethylene concentration on turnover frequency for a liquid feed stream of 30%wt. MeOH:MeP and 10%vol. CO in the gas feed at 100oC, 10bara.

6.3.3 Dependence of Reaction Rate on Carbon Monoxide Concentration

The effect of carbon monoxide concentration on the reaction rate was

investigated by keeping constant the liquid concentration in the feed at

30%wt. MeOH:MeP while ethylene concentration in the feed was always

constant at 50%vol. Carbon monoxide concentration in the feed was ranged

between 5-40%vol. by means of an inert diluting gas, helium. Gas and liquid

flowrates were kept constant in all cases at 0.1ml25oC,10bara/min and

0.005ml/min respectively. The experimental conditions for the carbon

monoxide series experiments are shown in Table 6-3.

In Figure 6.4 the data which reflect the measured dependence of reaction rate

on carbon monoxide concentration in the outlet of the reactor are presented

graphically.


Page 146

Table 6-3 Experimental conditions for the carbon monoxide series experiments.

Temperature: 100oC

Pressure: 10bara

CO feed partial pressure: 0.5-4bara






Figure 6.4 Effect of carbon monoxide concentration on turnover frequency for a liquid feed stream of 30%wt. MeOH:MeP and 50%vol. C2H4 in the gas feed at

100oC, 10bara.

In previous studies of this reaction system, negative effect of carbon

monoxide concentration on reaction rate has been observed at high carbon

monoxide concentrations due to poisoning of the catalyst by carbon

monoxide species [192,193]. The decomposition reaction is believed to occur


Page 147

when carbon monoxide reacts with the palladium hydride complex before

ethylene addition as shown in equations (6.2)-(6.5).

(𝐿 − 𝐿)𝑃𝑑(𝐻)]+ + 𝐶𝑂𝐾1↔ (𝐿 − 𝐿)𝑃𝑑(𝐻)(𝐶𝑂) (6.2)

(𝐿 − 𝐿)𝑃𝑑(𝐻)(𝐶𝑂) + 𝐶𝑂𝐾2↔ (𝐿 − 𝐿)𝑃𝑑(𝐶𝑂)2 + 𝐻+ (6.3)

(𝐿 − 𝐿)𝑃𝑑(𝐶𝑂)2 + 𝐶𝑂𝐾3↔ (𝐿 − 𝐿)𝑃𝑑(𝐶𝑂)3 (6.4)

(𝐿 − 𝐿)𝑃𝑑(𝐶𝑂)3 + 𝐶𝑂𝐾4↔ 𝑃𝑑(𝐶𝑂)4 ↓ (6.5)

This rapidly leads to reduction of the palladium to palladium (0) which has a

greater tendency to form clusters. Similar deactivation of the catalyst by

carbon monoxide molecules has been reported in other reactions such as the

hydroformulation of ethylene using a Rd-complex catalyst [194,195], the

hydroformulation of 1-decane using a Rd-complex catalyst [190].

However no sign of catalyst poisoning by carbon monoxide appeared in our

study most probably because of the very high catalyst concentrations used in

this study (about 10 times larger than in previous studies [192,193]. This

means that if there were any loss of catalyst due to poisoning it would be

unlikely to impact the rate very much.

6.3.4 Dependence of Reaction Rate on Temperature

A series of experiments was conducted in order to establish the temperature

effect on the reaction rate. The experimental conditions for the carbon

monoxide series experiments are shown in Table 6-4. The reactor

temperature range investigated was between 80-120oC. In all cases the liquid

feed composition was 30:70%wt. MeOH:MeP while the gas feed composition

was 10%wt. CO:C2H4. Gas and liquid flowrates were kept constant in all

cases at 0.1ml25oC,10bara/min and 0.005ml/min respectively.


Page 148

Table 6-4 Experimental conditions for the temperature series experiments.

Temperature: 80-120oC

Pressure: 10bara







The results of the temperature effect series are shown in Figure 6.5.

Figure 6.5 Effect of temperature on turnover frequency for a liquid and gas feed stream of 30%wt. MeOH:MeP and 10%vol.CO:C2H4 respectively at 10bara.

The turnover frequency increases when increasing the temperature of the

reactor (and hence decreasing 1/T). However, it should be noted that when

the temperature changes the composition in the gas and the liquid changes

according to the new vapour liquid equilibrium. Hence, these observations


Page 149

are a result of the temperature change as well as the gas and liquid

composition change.

6.4 Kinetic Modeling and Parameter Estimation

6.1 Reaction Mechanism and Kinetic Models Discretisation

There are three possible kinetic models for the formation of methyl

propionate based on the Pd-Hydride cycle (Figure 6.6) [196].

Figure 6.6 Palladium-Hydride catalytic cycle for the formation of methyl propionate.

This depends on which reaction step (i.e the methanolysis step, the addition

of ethylene or the addition of carbon monoxide) we consider as the rate

determining step. All three kinetic models will be developed and examined

with respect to how well they fit the experimental observations and data of

the system.

The main assumptions for these models are the following:

The Pd-Hydride cycle (Figure 6.6) is the predominant cycle [196].

The reverse reaction of the MeP decomposition resulting in the

formation of CO, C2H4 and MeOH is negligible.

The quasi-state approximation was used for the analysis which

assumes that the intermediate complexes formed are very reactive

and they never accumulate to considerable amounts compared to the


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concentrations of the main reactants (i.e. carbon monoxide, ethylene

and methanol).

6.4.1.1 Carbon Monoxide Addition the Rate Determining Step

First we examine the case of carbon monoxide addition being the rate

limiting step. Below the suggested reaction scheme is presented where the

various complexes were named with letters (i.e. a-c) for simplicity.

[(𝐿 − 𝐿)𝑃𝑑(𝐻)]+ + 𝐶2𝐻4

𝐾1↔ [(𝐿 − 𝐿)𝑃𝑑(𝐶𝐻2𝐶𝐻3)]+ (6.6)

(a) (b)

[(𝐿 − 𝐿)𝑃𝑑(𝐶𝐻2𝐶𝐻3)]+ + 𝐶𝑂𝑘2→ [(𝐿 − 𝐿)𝑃𝑑(𝐶𝑂)(𝐶𝐻2𝐶𝐻3)]+ (6.7)

(b) (c)

[(𝐿 − 𝐿)𝑃𝑑(𝐶𝑂)(𝐶𝐻2𝐶𝐻3)]+ + 𝐶𝐻3𝑂𝐻𝐾3↔ [(𝐿 − 𝐿)𝑃𝑑(𝐻)]+

+ 𝐶𝐻3𝐶𝐻2𝐶𝑂𝑂𝐶𝐻3 (6.8)

(c) (a)

Analysis using the steady state approximation for reactions (6.28)-(6.30)

gives,

𝐾1 =

[𝑏]

[𝑎] ∙ [𝐶2𝐻4] (6.9)

𝐾3 =

[𝑎]

[𝑐] ∙ [𝐶𝐻3𝑂𝐻] (6.10)

𝑅 = 𝑘2 ∙ [𝑏] ∙ [𝐶𝑂] (6.11)

[𝑃𝑑] = [𝑎] + [𝑏] + [𝑐] (6.12)

where [a], [b] and [c] are the concentrations of species (a), (b) and (c) of

reactions (6.28)-(6.30) and [Pd] is the concentration of Palladium catalyst in


Page 151

the system. After rearranging and combining equations (6.31)-(6.34) the

following reaction rate expression is formed,

𝑅 =

𝑘2 ∙ 𝐾1 ∙ 𝐾3 ∙ [𝑃𝑑] ∙ [𝐶𝑂] ∙ [𝐶2𝐻4] ∙ [𝐶𝐻3𝑂𝐻]

1 + 𝐾3 ∙ [𝐶𝐻3𝑂𝐻] + 𝐾1 ∙ 𝐾3 ∙ [𝐶𝐻3𝑂𝐻] ∙ [𝐶2𝐻4] (6.13)

When setting 𝑧 = 𝐾3 ∙ [𝐶𝐻3𝑂𝐻] + 𝐾1 ∙ 𝐾3 ∙ [𝐶𝐻3𝑂𝐻] ∙ [𝐶2𝐻4] in the

denominator, two cases are possible for equation (6.13). If z>>1, equation

(6.13) becomes,

𝑅 =

𝑘2 ∙ 𝐾1 ∙ 𝐾3 ∙ [𝑃𝑑] ∙ [𝐶𝑂] ∙ [𝐶2𝐻4] ∙ [𝐶𝐻3𝑂𝐻]

𝐾3 ∙ [𝐶𝐻3𝑂𝐻] + 𝐾1 ∙ 𝐾3 ∙ [𝐶𝐻3𝑂𝐻] ∙ [𝐶2𝐻4]

=𝑘2 ∙ 𝐾1 ∙ 𝐾3 ∙ [𝑃𝑑] ∙ [𝐶𝑂] ∙ [𝐶2𝐻4]

𝐾3 + 𝐾1 ∙ 𝐾3 ∙ [𝐶2𝐻4]

(6.14)

In this case, the effect of methanol on the reaction rate is cancelled out.

However, this is not in agreement with the experimental observations where

a positive effect of methanol on the reaction rate was observed.

If z<<1, , equation (6.13) becomes,

𝑅 =

𝑘2 ∙ 𝐾1 ∙ 𝐾3 ∙ [𝑃𝑑] ∙ [𝐶𝑂] ∙ [𝐶2𝐻4] ∙ [𝐶𝐻3𝑂𝐻]

1 (6.15)

In this case, the model suggests a positive ethylene effect on the reaction rate.

However, experimentally no effect of ethylene on the reaction rate was

reported. Hence, it can be concluded that this kinetic expression is not

suitable for the representation of this system and consequently, the addition

of carbon monoxide is not the rate determining step based on the

experimental data.

6.4.1.2 Ethylene Addition the Rate Determining Step

When considering the case of ethylene addition being the rate limiting step,

the reaction scheme is the following:


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[(𝐿 − 𝐿)𝑃𝑑(𝐻)]+ + 𝐶2𝐻4

𝑘1→ [(𝐿 − 𝐿)𝑃𝑑(𝐶𝐻2𝐶𝐻3)]+ (6.16)

(a) (b)

[(𝐿 − 𝐿)𝑃𝑑(𝐶𝐻2𝐶𝐻3)]+ + 𝐶𝑂𝐾2↔ [(𝐿 − 𝐿)𝑃𝑑(𝐶𝑂)(𝐶𝐻2𝐶𝐻3)]+ (6.17)

(b) (c)

[(𝐿 − 𝐿)𝑃𝑑(𝐶𝑂)(𝐶𝐻2𝐶𝐻3)]+ + 𝐶𝐻3𝑂𝐻𝐾3↔ [(𝐿 − 𝐿)𝑃𝑑(𝐻)]+


(c) (a)


gives,

𝐾2 =

[𝑐]

[𝑏] ∙ [𝐶𝑂] (6.19)

𝐾3 =

[𝑎]

[𝑐] ∙ [𝐶𝐻3𝑂𝐻] (6.20)

𝑅 = 𝑘1 ∙ [𝑎] ∙ [𝐶2𝐻4] (6.21)

[𝑃𝑑] = [𝑎] + [𝑏] + [𝑐] (6.22)

Where [a], [b] and [c] are the concentrations of species (a), (b) and (c) of




𝑅 =

𝑘1 ∙ 𝐾2 ∙ 𝐾3 ∙ [𝑃𝑑] ∙ [𝐶𝑂] ∙ [𝐶2𝐻4] ∙ [𝐶𝐻3𝑂𝐻]

1 + 𝐾2 ∙ [𝐶𝑂] + 𝐾2 ∙ 𝐾3 ∙ [𝐶𝑂] ∙ [𝐶𝐻3𝑂𝐻] (6.23)

This is not a suitable rate expression as it suggests positive effect of ethylene

while experimentally ethylene found to have no effect on the reaction rate.


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Hence, it can be concluded that the addition of ethylene is not the rate

determining step based on the experimental data.

6.4.1.3 Methanolysis the Rate Determining Step

Assuming that the methanolysis is the rate limiting step, the corresponding

reaction scheme is,

[(𝐿 − 𝐿)𝑃𝑑(𝐻)]+ + 𝐶2𝐻4

𝐾1↔ [(𝐿 − 𝐿)𝑃𝑑(𝐶𝐻2𝐶𝐻3)]+ (6.24)

(a) (b)

[(𝐿 − 𝐿)𝑃𝑑(𝐶𝐻2𝐶𝐻3)]+ + 𝐶𝑂

𝐾2↔ [(𝐿 − 𝐿)𝑃𝑑(𝐶𝑂)(𝐶𝐻2𝐶𝐻3)]+ (6.25)

(b) (c)

[(𝐿 − 𝐿)𝑃𝑑(𝐶𝑂)(𝐶𝐻2𝐶𝐻3)]+ + 𝐶𝐻3𝑂𝐻𝑘3→ [(𝐿 − 𝐿)𝑃𝑑(𝐻)]+


(c) (a)


gives,

𝐾1 =

[𝑏]

[𝑎] ∙ [𝐶2𝐻4] (6.27)

𝐾2 =

[𝑐]

[𝑏] ∙ [𝐶𝑂] (6.28)

𝑅 = 𝑘3 ∙ [𝑐] ∙ [𝐶𝐻3𝑂𝐻] (6.29)

[𝑃𝑑] = [𝑎] + [𝑏] + [𝑐] (6.30)

Where [a], [b] and [c] are the concentrations of species (a), (b) and (c) of





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𝑅 =

𝑘3 ∙ 𝐾1 ∙ 𝐾2 ∙ [𝑃𝑑] ∙ [𝐶𝑂] ∙ [𝐶2𝐻4] ∙ [𝐶𝐻3𝑂𝐻]

1 + 𝐾1 ∙ [𝐶2𝐻4] + 𝐾1 ∙ 𝐾2 ∙ [𝐶2𝐻4] ∙ [𝐶𝑂] (6.31)

This is a suitable rate expression as it is in agreement with the experimental

observation such as the positive effect of methanol.

6.2 Parameter Estimation

Using the kinetic model (6.31), the validated reactor model (Chapter 5.5) and

the experimental data, parameter estimation of the kinetic model was

performed using gPROMS. However, it was not possible to identify the

model parameters of the kinetic model in the current form. A model is

practically identifiable when each set of model parameters can be uniquely

determined by each set of experiments [197,198]. For this purpose, the kinetic

model was reparametrised to (6.32) in order to decrease the number of

parameters and cancel any correlation problems.

𝑅 =

𝐶 ∙ [𝑃𝑑] ∙ [𝐶𝑂] ∙ [𝐶2𝐻4] ∙ [𝐶𝐻3𝑂𝐻]

1 + 𝐴 ∙ [𝐶2𝐻4] + 𝐵 ∙ [𝐶2𝐻4] ∙ [𝐶𝑂] (6.32)

where, A=K1, B=K1∙K2, C=K1∙K2∙k3.

Even after the reparametrisation numerical problems prevented the

parameter estimation to reach a solution. A possible reason for these

numerical problems is the fact that we are dealing with very small numbers

(~10-15) due to the small concentrations in the liquid phase. In addition, it is

noteworthy that gPROMS considers numbers smaller than 10-22 equal with

zero. Hence, in order to prevent any numerical problems, it was decided to

replace the concentrations in (6.32) with molar fractions ( 𝐶𝑖 = 𝑥𝑖 ∙ 𝐶𝑡𝑜𝑡𝑎𝑙 )

resulting to (6.33).


Page 155

𝑅 = (𝐶 ∙ 𝑃𝑑 ∙ 𝑥𝐶𝑂 ∙ 𝑥𝐶2𝐻4

∙ 𝑥𝐶𝐻3𝑂𝐻

𝐴 ∙ 𝑥𝐶2𝐻4+ 𝐵 ∙ 𝑥𝐶2𝐻4

∙ 𝑥𝐶𝑂 ∙ (𝐹ℓ,𝑡𝑜𝑡𝑎𝑙

𝜐ℓ) + (

𝜐ℓ

𝐹ℓ,𝑡𝑜𝑡𝑎𝑙)

) ∙ (𝐹ℓ,𝑡𝑜𝑡𝑎𝑙

𝜐ℓ)

2

(6.33)

Furthermore, in order to work with even larger numbers which would result

in a smoother simulation, the reparametrised reaction rate, RR, was used for

the parameter estimation (6.34).

𝑅 = 10−9 ∙ 𝑅𝑅 (6.34)

It should be clarified that this reparametrisation did not affect the actual

results of the parameter estimation of the kinetic model as the kinetic

expression, R, remained the same. It was only a modification to help the

parameter estimation solver work more efficiently by avoiding working with

very small numbers.

Another similar modification of the parameter estimation system was the

reparametrisation of the parameters under estimation in order their values to

be close to 1. This reparametrisation helps greatly the solver for a better

performance by avoiding working with very small numbers. Hence, instead

of estimating parameter A, B and C, the new parameter for estimation were

theta1, theta2 and theta3 according to (6.35)-(6.37).

𝐴 = 𝐴𝐴𝑛 ∙ 𝑡ℎ𝑒𝑡𝑎1 (6.35)

𝐵 = 𝐵𝐵𝑛 ∙ 𝑡ℎ𝑒𝑡𝑎2 (6.36)

𝐶 = 𝐶𝐶𝑛 ∙ 𝑡ℎ𝑒𝑡𝑎3 (6.37)

where AAn=105, BBn=1015, CCn=2∙1018.

After these modifications, estimation of the parameters theta1, theta2 and

theta3 was performed by means of the collected kinetic data, the reactor

model and (6.33)-(6.37). Statistically satisfactory fit of the experimental data


Page 156

was obtained based on the parameter estimation. The parity plot of the data

fit is shown in Figure 6.7. The fit between the experimental data of reaction

rate and the corresponding predictions based on the suggested kinetic model

in the whole design space is satisfactory. Detailed comparison of the model

predictions with the experimental data can be found in the Appendix J.

Figure 6.7 Parity plot of experimental and predicted from the kinetic model reaction rate data.

In order to statistically assess the reliability and adequacy of the model and

of the new parameter estimates, a 𝜒2-test was performed considering the

sum of the weighted residuals [199],

𝑆𝑊𝑅 = ∑ [(𝑦𝑖 − �̂�𝑖) ∑ (𝑦𝑖 − �̂�𝑖)

−1

𝑖]

𝑁

𝑖=1

(6.38)

,where 𝑦𝑖is the measured data and �̂�𝑖 is the predicted ones.

This SWR value was compared with a reference 𝜒2distribution with (n-p)

degrees of freedom (n is the total number of data, p is the total number of

parameters). If the 𝑆𝑊𝑅 value < 𝜒2distribution implies an adequate fit of the

model to the experimental data. This is because it indicates that any

deviations between the predictions and the experimental data can be solely


Page 157

attributed to measurement errors. In that case the model can adequately

describe the physical system under investigation. In our case, the SWR value

and 𝜒2distribution were calculated automatically in gPROMS in the end of

the parameter estimation process by a built-in statistical tool. It was found

that SWR value was much smaller than the 𝜒2distribution, confirming the

excellence of the data fit.

The corresponding estimated values of the kinetic model parameters, theta1,

theta2 and theta3 are shown in Table 6-5.

Table 6-5 Estimation results of parameters of kinetic model.

Parameter Final Value Standard Deviation 95% t-value

theta1 9.798∙10-6 5∙10-6 1.701

theta2 0.1049 0.0048 10.88

theta3 0.0041 0.0002 10.94

Reference t-value (95%) 1.680

The standard deviation of each model parameter was calculated based on,

𝜎𝑖 = √∑ (𝑋𝑖 − 𝑥)2𝑁

𝑗=1

𝑁 − 1 (6.39)

where N is the number of experiments, 𝑋𝑖 is the simulation response and x is

the measured response. In the fourth column, the t-value of the estimation

results is shown for 95% confidence.

The t-values are a common way to measure the confidence of the model

parameter estimates and are evaluated as,

𝑡𝑖 =

𝜃�̂�

√𝑉𝑖𝑖

(6.40)

where 𝑉𝑖𝑖 is variance of the i-th element (the i-th element of the diagonal

element of the variance-covariance matrix) and 𝜃𝑖 is the vector of the current

parameter estimates. The t-values are compared to a reference t-value,

usually given by a Student t-distribution with (n-p) degrees of freedom (n is


Page 158

the total number of data, p is the total number of parameters). If the t-value

of a given model parameter is higher than the reference t-value, the estimate

is reliable. Very high t-values usually indicate a high confidence in the

estimation of the parameters [200].

In our case, the t-values of all model parameters were calculated by means of

a built-in statistical tool of gPROMS. The estimation of all parameters

appears to be satisfactory as their t-value is larger than the reference t-value.

Based on the estimated parameters in Table 6-5, the equilibrium constants

K1, K2 and the kinetic constant k3 were calculated in Table 6-6.

Table 6-6 Estimation results of original parameters of kinetic model.

Parameter Value

K1 (ml/mol) 9.79∙104

K2 (ml/mol) 1.071∙109

k3 (ml/mol/min) 7.913∙101

The results show that K2>K1 indicating the limited effect of ethylene effect on

reaction rate.

6.3 Sensitivity Analysis

In kinetic modelling, when the aim is to fit a model to experimental data and

to establish the best parameter estimates, it is essential to evaluate how much

a variation of the estimated parameter vector affects the predicted measured

response of the model. For this process the sensitivity analysis of the system

is the ideal analysis tool as it gives the effect of a variation of a model

parameter on a measured response based on the sensitivity coefficients

matrix, qi, defined in (6.41) [200].


Page 159

𝑞𝑖 = [

𝜕𝑥𝑖

𝜕𝜃𝑖] (6.41)

where x are the measured responses and θ are the model parameters.

The sensitivity analysis of a parameter shows how important this parameter

is in the calculation of a response and how easy it is to estimate this

parameter. A large effect of the variation of a model parameter on the

response indicates that this parameter can be easily estimated.

Sensitivity analysis of parameter theta1 was done by varying the value of

parameter theta1 relatively to its actual value (while keeping theta2 and

theta 3 fixed) and measuring the effect of this variation on the reaction rate.

Similarly, sensitivity analysis was performed for parameters theta2 and

theta3 as well. The results are presented in Figure 6.8.

Figure 6.8 Sensitivity analysis of parameters theta1, theta2 and theta3 on reaction rate.

The sensitivities of all three parameters are very small- the largest one is of

parameter theta3 and does not exceed 2∙10-4. The small values of sensitivities


Page 160

especially for parameter theta1 and theta2 indicate that their estimation is

not very easy as their effect on the measured response (the reaction rate in

our case) is not significant. Possible ways to improve the sensitivity of the

model parameters is by model reformulation and reparametrisation.

6.4 Information Analysis

Another very valuable analysis tool in the kinetic modelling is the

information analysis of the system. This consists of the study of the

information each experiment provides with regards to the estimation of a

parameter in our case. The information which can be acquired by each single

experiment can be represented by the measure of Fisher Information Matrix

(FIM), 𝐻𝜃 , which is built from the sensitivity matrix and the preliminary

information matrix as shown in(6.42) [200].

𝐻𝜃(𝜃, 𝜑) = [∑ ∑ ∑ 𝑠𝑖𝑗𝑘 ∙ 𝑄𝑖𝑘𝑇 ∙ 𝑄𝑗𝑘 + 𝐻𝜃

0

𝑁𝑦

𝑗=1

𝑁𝑦

𝑖=1

𝑛𝑠𝑝

𝑘=1

] (6.42)

where θ are the model parameters, φ is the design vector, 𝑠𝑖𝑗𝑘 is the variance-

covariance of measurements errors, 𝑄𝑖𝑘𝑇 ∙ 𝑄𝑗𝑘 is the sensitivity matrix, 𝑁𝑦 is

the number of measured variables, 𝑛𝑠𝑝 is the number of experiments and 𝐻𝜃0

the prior information matrix, taking into account the statistical information

about the parametric system before each trial is carried out. The scope of the

design procedure is the maximisation of the expected information predicted

by minimising a metric ψ of the variance-covariance matrix of model

parameters. The most commonly used design criteria are the so called

‘alphabetic criteria’ [200] (reference: Federico thesis, 2. Kiefer 1959). The

geometrical interpretation of the alphabetic design criteria for a two

parameters problem is shown in Figure 6.9.

In the case of A-optimality the trace of information matrix is considered

while in the case of D-optimal and E-optimal the determinant and the

maximum eigenvalue of the FIM are considered respectively [200]. The


Page 161

information analysis of a system is a very powerful analysis tool as it

provides insights on how informative the experiments are and which

experiments are more important.

Figure 6.9 Design Criteria for model-based design of experiments.

Information analysis was conducted on the already performed experiments

by plotting the trace of Fischer Information Matrix based on the A-optimal

design, calculated in gPROMS, for each experiment. The results of the

information analysis are presented in Figure 6.10 where the information

provided by the different series of experiments for the estimation of the

kinetic parameter is given. This is based on (6.42) for one experiment.

The most informative experiments appear to be those studying the carbon

monoxide effect (Figure 6.10). Then, the next most informative are those

studying the ethylene effect. The least informative experiments are those

studying the methanol effect. It is interesting to note also that in all series of

experiments there are experiments that provide almost zero information.


Page 162

These experiments could have been avoided if the experiments were

designed based on their information content.

Figure 6.10 Information analysis of performed experiments based on Fischer information.

6.5 Conclusions

The kinetics of methoxycarbonylation of ethylene was studied in this chapter

using a capillary reactor and the effect of methanol, ethylene and carbon

monoxide concentration on the reaction rate was investigated. Methanol

found to have a great, positive effect on the observed reaction rate although

it was in excess. This may indicate that methanol insertion is not favoured

and hence a higher concentration in solution increases the chance of an

attack of methanol on the complex and influences the overall reaction rate in

this way. On the contrary, ethylene appeared to have no significant effect on

the reaction rate. This was attributed to its high solubility and the fast mass

transfer of the system. Similar behaviour was also reported by Seayad [191]

who studied the carbonylation of styrene using a homogenous Pd-complex


Page 163

catalyst and observed zero-order with respect to the styrene. Carbon

monoxide found to have a positive effect on the reaction rate. This is not in

agreement with previous studies, where a negative effect of carbon

monoxide was observed for very high carbon monoxide concentrations due

to poisoning of the catalyst by carbon monoxide species [192]. However no

sign of catalyst poisoning by carbon monoxide appeared in our study most

probably because of the very high catalyst concentrations used in this study

(about 10 times larger than in previous studies [192,193]. This means that if

there were any loss of catalyst due to poisoning it would be unlikely to

impact the rate very much. Temperature increase found also to increase the

turnover frequency.

A mechanistic kinetic model that can describe satisfactorily the system’s

behaviour was developed based on the Palladium hydride catalytic cycle.

Kinetic model discretisation was performed based on the experimental

observations and it was concluded that methanolysis is the rate-controlling

step in this reaction system. Parameter estimation of the kinetic model was

performed and excellent fit of data was achieved. The results showed that

the addition of carbon monoxide is more favourable than the ethylene

insertion. The accuracy of the estimation was validated using statistical tools.

Information analysis was conducted on the already performed experiments

by plotting the trace of Fischer Information Matrix based on the A-optimal

design. It was found that the most informative experiments are those

studying the carbon monoxide effect, then those studying the ethylene effect

and finally, the least informative experiments, those studying the methanol

effect.

CHAPTER 7. Conclusions & Future Developments

Page 164


The first part of the thesis (Chapter 3) focused on the development of a

mathematical model for the simulation of gas-liquid reactions in capillary

microreactors. A one-dimensional plug flow reactor model was developed

and its validation was performed with experiments with a model system,

carbon dioxide absorption in a sodium carbonate/bicarbonate buffer

solution, a system with well-studied kinetics. A flow set-up was designed

and built for the study of the model reaction and design of the operating

condition was conducted in order the system to operate under kinetic

control.

Flow observation of the system was performed by means of a high-speed

camera and the flow pattern found to be slug-annular with long gas bubbles

and thin liquid slugs in between. Bubble length found to increase with

increase of the gas flowrate or with decrease of the capillary size. Moreover,

the liquid film around the gas bubble found to became thicker when the gas

flowrate increased (and hence as the capillary number increases), consistent

with previous observations of Taylor and Bretherton [174,175]. Mass transfer

resistances in this system were negligible based on Hatta criterion (Ha<0.3).

The flow was found to deviate slightly from the ideal plug-flow behaviour

based on residence time distribution experiments and this deviation

increased when increasing the gas-to-liquid ratio. Furthermore, it was

observed that the numerical void fraction prefactor A, necessary for the

determination of the liquid volume fraction, was not constant as the gas-to-

liquid ratio increased, but gradually increased. This highlights the

importance of measuring experimentally the void fraction and the residence

time of a multiphase system rather than using correlations especially when

operating under conditions (channels with different geometrical

characteristics, different fluids, or different gas-to-liquid rations) different

from those in the studies of these correlations.


Page 165

Experiments were conducted under different gas-to-liquid ratios and

temperatures and using glass microcapillaries with different inner diameters.

Results showed that carbon dioxide conversion decreased with increasing

gas flowrate (while keeping the liquid flowrate constant) due to the decrease

of the volume fraction and residence time. At constant gas and liquid

flowrates, higher conversion of carbon dioxide was observed at higher

temperatures due to the higher reaction rate constant at higher temperature.

Comparison of the obtained results with the corresponding reactor’s model

predictions showed good agreement, confirming that this reactor model can

be used with confidence for the evaluation of the kinetics of other similar

gas-liquid catalytic reaction systems in capillary microreactors under slug-

annular flow.

In Chapter 4, the hydrodynamic study of gas-liquid systems with very small

gas and liquid velocities in capillary microreactors was discussed. Optical

sensors were integrated in the flow set-up to perform residence time

distribution (RTD) experiments and a microscope camera was used for the

flow observation of the gas-liquid systems. Three gas-liquid systems

(N2/water, methanol and 10% aqueous glycerol solution) were studied in

PFA microcapillaries of various inner diameters (0.25, 0.5 and 1mm) under

different gas-to-liquid ratios (0.66-40). Gas and liquid superficial velocities

were varied between 0.004-0.068m/s and 0.0001-0.102m/s respectively.

At high gas-to-liquid ratios, the N2/methanol system presented much larger

gas bubbles compared to the N2/water system. This was due to the increased

contact angle of water on the PFA surface that prevented the further

spreading of the liquid on the wall and led to the formation of frequent,

short slugs. Moreover, the transition from slug flow to slug-annular flow

moved to lower gas-to-liquid ratios with decreasing surface tension, in

agreement with previous studies [82,96,179-181]. As the gas-to-liquid

flowrate ratio increased, axial dispersion in the system increased, behaviour

also reported by Kreutzer et al. [182]. This was explained by the fact that


Page 166

when the gas-to-liquid ratio was very large, the liquid slugs were very short

and followed by very long gas bubbles. This was leading to incomplete

mass-exchange with the stagnant liquid film causing excessive broadening of

the step change. In the case of the N2/water system, it was found that axial

dispersion became noticeable for gas-to-liquid ratios above 5. When

increasing the viscosity of the liquid, less axial dispersion was observed in

the system, behaviour also reported by Zhang et al. [179]. This was

attributed to the thicker film that was formed around the bubble at higher

viscosities, as the driving force of the gas to break through a more viscous

liquid was larger leading to a smaller dispersion number [174,184,185]. This

difference on dispersion numbers between two fluids with different

viscosities was found to become larger for smaller liquid flowrates, hence at

large gas-to-liquid ratios. This was because at large gas-to-liquid flowrates

the flow pattern moved to a more annulus-type flow pattern where the film

thickness became a more critical parameter for mass transfer in the capillary.

By increasing the tube diameter, less dispersion was observed in the system

and the flow approached a more plug flow type behaviour. This was because

for the same gas and liquid flowrates, the superficial velocities were smaller

in capillaries with larger diameters resulting to smaller Reynolds and

capillary numbers leading to smaller dispersion numbers [183,185].

Experimental data of void fraction of a N2/water system in capillaries with

various inner diameters (0.25-1mm) in a range of gas-to liquid ratios (0.3-400)

showed that the void fraction was not strongly dependent on the inner

diameter of the capillary in this range of diameters. The void fraction data of

this system were well described by homogenous model at high volumetric

qualities (β>0.65) and by Armand model for moderate volumetric qualities

(0.65>β>0.45). As the volumetric quality decreased below 0.45, the void

fraction deviated largely from both models and no other hydrodynamic

model was well predictive either. For this purpose, a new correlation was


Page 167

developed which found to fit the full set of void fraction data with great

accuracy.

It was observed that the nature of the liquid affected the void fraction only in

very small gas-to-liquid ratios, when the amount of liquid in the system was

significant. The lower the surface tension of the liquid, the larger the void

fraction of the system found to be for certain gas and liquid velocities.

Future study should include residence time distribution studies of more gas-

liquid systems in capillaries with various diameters and at various gas and

liquid velocities. This would allow the development of a universal

correlation for the void fraction in microcapillaries, independent of the gas-

to-liquid ratio or the nature of the fluids. Moreover, flow observation of

these systems by means of a high speed camera would allow the creation of

universal flow maps which is not available in the literature for small gas and

liquid velocities.

Chapter 5 focused on the design of the set-up and the analysis methodology

for the study of methoxycarbonylation of ethylene. Design of reactor’s

material was based on permeability and reactivity experiments. Hastelloy

was concluded to be the most suitable reactor’s material as it was found to be

non-permeable and it provided an inert and hence non-reactive internal

surface. Vapour-liquid equilibrium (VLE) of the system was accounted by

means of a pre-existing VLE model developed for this system and its validity

was tested with experimental data. A gas-to-liquid ratio of 23 was chosen for

the kinetic study based on RTD experiments as it provided enough residence

time for the reaction and resulted to plug flow behaviour. The system was

under kinetic control at these conditions based on Hatta criterion.

Further study should include experimental study of liquid pretreatment with

ethylene on the reaction performance and on catalyst poisoning by carbon

monoxide. Moreover, the effect of reactor’s material on reaction performance

is another very interesting topic to investigate by testing the reaction


Page 168

performance in capillaries of different materials such as stainless steel,

titanium and aluminium. This would give us valuable knowledge on the

surface effects (e.g. reaction between surface and catalyst, precipitation of

catalyst on the surface) of these materials and their implication on catalyst

performance.

In Chapter 6, the kinetic study of methoxycarbonylation of ethylene was

performed using the experimental set-up and the analysis methodology

described in Chapter 5. The reactants’ concentrations and temperature effect

on the reaction rate was investigated. Methanol was found to have a great

effect on the observed reaction rate, with an order close to unity, although it

was in excess. This may indicate that in the catalytic cycle methanol insertion

is not favoured and hence a higher concentration of methanol increases the

chance of an attack of methanol on the catalytic complex and influences the

overall reaction rate in this way. On the contrary, ethylene appeared to have

no significant effect on the reaction rate. This was attributed to its high

solubility and the fast mass transfer of the system. Similar behaviour was

also reported by Seayad [191] who studied the carbonylation of styrene

using a homogenous Pd-complex catalyst and observed zero-order with

respect to the styrene. Carbon monoxide was found to have a positive effect

on the reaction rate. This is not in agreement with previous studies, where a

negative effect of carbon monoxide was observed for very high carbon

monoxide concentrations due to poisoning of the catalyst by carbon

monoxide species [192]. However no sign of catalyst poisoning by carbon

monoxide appeared in our study most probably because of the very high

catalyst concentrations used in this study (about 10 times larger than in

previous studies [192,193]). This means that if there were any loss of catalyst

due to poisoning it would be unlikely to impact the rate very much.

Temperature increase was also found to increase the turnover frequency.

Future work on the kinetics of methoxycarbonylation of ethylene should

include a more in-depth investigation of the temperature effect on the


Page 169

parameters of the kinetic model by performing a number of experiments at

different inlet reactants’ concentrations at different temperature conditions.

Another very interesting topic to investigate further would be that of catalyst

deactivation due to carbon monoxide poisoning at high carbon monoxide

concentrations using different catalyst concentrations. This would give

valuable information on the mechanism related to the catalyst deactivation,

essential for further optimisation of the process.

Moreover, in Chapter 6 a kinetic model based on palladium hydride catalytic

cycle was suggested to describe the mechanism of this system. Kinetic model

discretisation was performed based on the experimental observations and it

was concluded that methanolysis is the rate-controlling step in this reaction

system. Parameter estimation of the model was performed in gPROMS and

excellent fit of data was achieved in the whole design space indicating that it

is a suitable model for this system. The accuracy of the estimation was

validated using gPROMS built-in statistical tools.

Lucite International can be immediately benefited by the results of this

study, especially the knowledge of the kinetic behaviour of this system and

the development of a kinetic model that is aligned with the reaction

mechanism of the system and the experimental data. These results can be

used to understand better the process, redesign the reactors accordingly and

optimise further the process.

Moreover, this study can be further used at a higher level as an automated

methodology and tool for kinetic analysis of gas-liquid catalytic systems in a

much quicker and accurate way. The fidelity of this methodology is based on

the combined insight it can provide on the chemistry on the system taking

also into account the vapour-liquid equilibrium and the hydrodynamics of

the system.

Future study should focus on improving further this methodology by

integrating in-situ concentration analysis such as IR analysis in the inlet and


Page 170

outlet of the capillary reactor and possibly even in more points along the

reactor. This would provide information that in this study had to be

predicted based on reactor and VLE modelling and downstream

experimental measurements, increasing hence the complexity of the analysis.

Increase of the measurements would also increase significantly the

information content of the experiments which would improve the accuracy

of the kinetic study.

Another very interesting tool to further improve the methodology developed

in this study is to include Design of Experiments (DoE) techniques to

improve the accuracy of the parameters estimation and reduce significantly

the number of experiments required [200-203]. This can be done by

retrospectively testing all possible combinations of design variables and

select those that result in the most informative experiments based on Fisher

Information Matrix (FIM), which is built from the sensitivity matrix [200].

The operating conditions may include the temperature and pressure

conditions in the reactor, the inlet concentrations but also the reactor design

characteristics. A process diagram of the design of optimum experiments is

shown in Figure 7.1.

Figure 7.1 Process diagram for a design of experiments process.

Page 171

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Page 191

Appendix A

Calibration Graphs

The calibration lines for the mass flow controllers used in this study are

shown below.

Figure A. 1 Calibration line of MFC1 (up to 3ml/min) with N2.

Figure A. 2 Calibration line of MFC2 (up to 1ml/min) with 20 vol% CO2/N2.

Appendix A.Calibration Graphs

Page 192

Figure A. 3 Calibration line of MFC used with nitrogen for the hydrodynamic study.

Figure A. 4 Calibration line of CO MFC (up to 1ml/min) at NTP conditions (20oC, 1bar).


Page 193

Figure A. 5 Calibration line of ethylene MFC (up to 3ml/min) at NTP conditions (20oC, 1bar).

Figure A. 6 Calibration line of helium MFC (up to 3ml/min) at NTP conditions


Page 194

The calibration line of the pressure transducer used to monitor the pressure

in the reactor is presented below.

Figure A. 7 Calibration line of pressure indicator (up to 17bar) before the reactor using He.

The final conditions chosen for the analysis of the carbon dioxide absorption

in carbonate-bicarbonate buffer solutions are shown in Table A. 1. A typical

chromatograph of CO2/N2 analysis is shown in Figure A. 8, where the first

peak is of N2 and the second of CO2.

Table A. 1 GC operating conditions for the analysis of the model system.

Column Name HP-PLOT Q

Oven Temperature 75oC

Inlet Temperature 75oC

Carrier Gas Helium

Carrier Flowrate 5ml/min

Detector TCD

Filament Temperature 250oC

Make-up Flowrate 5ml/min

Reference Flowrate 20ml/min


Page 195

Figure A. 8 A typical chromatograph of 20 vol%CO2/N2.

The calibration lines of gc for the analysis of various gases are shown below.

Figure A. 9 Calibration line of gc for carbon dioxide analysis.

N2

CO2


Page 196

Figure A. 10 GC calibration line for analysis of carbon monoxide in gas phase.

Figure A. 11 GC calibration line for analysis of ethylene in gas phase.


Page 197

Figure A. 12 Gc calibration line for analysis of N2/He mixtures.

Figure A. 13 Gc calibration line for analysis of methanol in gas phase.


Page 198

Figure A. 14 Gc calibration line for analysis of methyl propionate in gas phase.

Figure A. 15 Gc calibration line for analysis of methanol in liquid phase.


Page 199

Figure A. 16 Gc calibration line for analysis of methyl propionate in liquid phase.

Page 200

Appendix B

Photos of Experimental Set-Up

Figure A. 17 Experimental set-up for the test of the efficiency of the glass microseparator on separating gas-liquid streams under different gas and liquid

flowrates by means of two metering valves in the gas and liquid exit to control the corresponding pressure difference.

Gas-Liquid inlet

Gas outlet

Metering valve of the gas side

Metering valve of the liquid side

Liquid outlets

Appendix B. Photos of Experimental Set-Up

Page 201

Figure A. 18 General view of experimental set-up used for the study of the model system.

Figure A. 19 Closer view of the experimental set-up (upstream) used for the study

of the model system .

MFCs

Syringe pump

Pulse dampener

Non-return valve

Pressure-relief valve

Pressure indicator

Pressure indicator

GC

MFCs Syringe pump

Water bath


Page 202

Figure A. 20 General view of the experimental set-up (downstream) for the analysis of the model reaction by means of a glass microseparator.

Figure A. 21 Closer view of one of the glass reactors (L=1m, ID=0.5mm) used for the model reaction study and the glass microseparator where gas was separated from

the liquid and then was analysed by GC.

Glass reactor

Glass microseparator

Liquid trap

Gas to GC

Glass reactor

Gas-Liquid inlet

Gas-Liquid outlet

Gas-liquid microseparator


Page 203

Figure A. 22 Closer view of the glass microseparator used for the study of the model reaction.

Figure A. 23 General view of the experimental set-up for the flow observation by means of a high speed camera.

Liquid outlet

Liquid outlet

Gas outlet

Gas-Liquid inlet

Glass reactor

High speed

camera

Gas-Liquid inlet

Observation window


Page 204

Figure A. 24 General view of the experimental set-up used for the study of MeP high pressure system.

Figure A. 25 Closer view of the experimental set-up used for the study of the MeP high pressure system (upstream).

Gases MFCs

CO detector

Pressure relief valve

Syringe pump


Page 205

Figure A. 26 Spiral reactor tested for the study of the MeP system.

Figure A. 27 Closer view of the experimental set-up of the MeP high pressure system (downstream).

Pressure sensor

Reactor inlet / outlet

Thermocouple of the

temperature controller

Spiral reactor

Hot plate

BPR

Liquid sample

Exit to ventilator for any trapped gas to the liquid

exit

Metering valves for

smooth liquid sampling

Liquid outlet

Separator’s g/l inlet

Gas outlet


Page 206

Figure A. 28 Photos of the set-up used for gc calibration of vapour MeOH. Bottle with MeOH bubbled with N2/He (on the left) and cooling bath used to maintain the

temperature constant (on the right).

Figure A. 29 Stainless steel reactor tested for the study of MeP system and metallic vessel used as an oil bath to heat the reactor.

Page 207

Appendix C

Experimental Data of Residence Time Distribution Experiments

Table A. 2 Raw RTD experimental data for N2/DI water system for 0.2ml/min gas flowrate and 0.02ml/min liquid flowrate.

tnorm (s) Fnorm tnorm (s) Fnorm tnorm (s) Fnorm tnorm (s) Fnorm tnorm (s) Fnorm

0 0 0.550718 0.020393 1.101435 0.701899 1.652153 0.996227 2.20287 0.999973 0.026225 4.01E-05 0.576942 0.025451 1.12766 0.746698 1.678378 0.996989 2.229095 0.999973 0.052449 0.000107 0.603167 0.0317 1.153885 0.786814 1.704602 0.997591 2.25532 0.999987 0.078674 0.000174 0.629392 0.03942 1.180109 0.8221 1.730827 0.998073 2.281544 0.999987 0.104899 0.000268 0.655616 0.048907 1.206334 0.852622 1.757051 0.998461 2.307769 0.999987 0.131123 0.000388 0.681841 0.060522 1.232558 0.878688 1.783276 0.998769 2.333994 0.999987 0.157348 0.000535 0.708066 0.074679 1.258783 0.900686 1.809501 0.999023 2.360218 1 0.183573 0.000709 0.73429 0.091807 1.285008 0.919059 1.835725 0.999224 2.386443 1 0.209797 0.000937 0.760515 0.112387 1.311232 0.934273 1.86195 0.999371 2.412668 1 0.236022 0.001231 0.786739 0.136861 1.337457 0.946797 1.888175 0.999505 2.438892 1 0.262246 0.001579 0.812964 0.16567 1.363682 0.957047 1.914399 0.999599 2.465117 1 0.288471 0.002021 0.839189 0.199136 1.389906 0.965397 1.940624 0.999679 2.491342 1 0.314696 0.002583 0.865413 0.237432 1.416131 0.972168 1.966849 0.999746 2.517566 1 0.34092 0.003278 0.891638 0.280505 1.442356 0.97764 1.993073 0.999799 2.543791 1 0.367145 0.004148 0.917863 0.328034 1.46858 0.98207 2.019298 0.999839 2.570016 1 0.39337 0.005232 0.944087 0.37935 1.494805 0.985629 2.045523 0.99988 2.59624 1 0.419594 0.006597 0.970312 0.433517 1.52103 0.988479 2.071747 0.999893 0.445819 0.008296 0.996537 0.489329 1.547254 0.990781 2.097972 0.99992 0.472044 0.01041 1.022761 0.545395 1.573479 0.992627 2.124197 0.999933 0.498268 0.013033 1.048986 0.600324 1.599704 0.994099 2.150421 0.999946 0.524493 0.016311 1.075211 0.652858 1.625928 0.995277 2.176646 0.99996

Appendix C. Experimental Data of Residence Time Distribution Experiments

Page 208

Table A. 3 Experimental data of residence time distribution experiments for N2/DI water system.

Exp Reactor length

D Vr υl υg Volumetric quality, β

Mean RT

Void fraction ε

D/uL

cm cm ml ml/min ml/min s 31_4 87 0.1 0.704979 0.005 0.2 0.97561 217.4199 0.974299 0.069104 31_5 87 0.1 0.704979 0.005 0.5 0.990099 73.17242 0.991351 0.235979 31_6 87 0.1 0.704979 0.005 1 0.995025 30.71876 0.996369 0.64919 31_7 87 0.1 0.704979 0.005 1.5 0.996678 27.75113 0.99672 0.775928 31_8 87 0.1 0.704979 0.005 2 0.997506 26.89757 0.996821 1.359412 31_9 93.5 0.1 0.75765 0.02 0.181818 0.900901 221.2285 0.902669 0.023441 31_10 93.5 0.1 0.75765 0.05 0.167926 0.770564 236.8411 0.7395 0.007572 31_11 93.5 0.1 0.75765 0.1 0.152905 0.604595 206.2997 0.546185 0.003983 31_12 93.5 0.1 0.75765 0.3 0.12945 0.301432 127.6534 0.15757 0.004683 31_13 93.5 0.1 0.75765 0.15 0.142857 0.487805 196.2758 0.352353 0.000542 31_14'' 97.5 0.1 0.790063 0.5 0.162075 0.244798 86.30805 0.08965 0.000965 31_15' 97.5 0.1 0.790063 0.25 0.168209 0.402212 139.9723 0.261808 0.001964 31_16 97.5 0.1 0.790063 0.07 0.136705 0.661354 240.6984 0.644567 0.002236 31_17 97.5 0.1 0.790063 0.03 0.157729 0.840195 190.6332 0.879356 6.82E-05 31_18 97.5 0.1 0.790063 0.13 0.166667 0.561798 194.8267 0.465708 0.000617 31_4 87 0.1 0.704979 0.005 0.2 0.97561 217.4199 0.974299 0.069104 31_5 87 0.1 0.704979 0.005 0.5 0.990099 73.17242 0.991351 0.235979 31_6 87 0.1 0.704979 0.005 1 0.995025 30.71876 0.996369 0.64919 31_7 87 0.1 0.704979 0.005 1.5 0.996678 27.75113 0.99672 0.775928 31_8 87 0.1 0.704979 0.005 2 0.997506 26.89757 0.996821 1.359412 31_9 93.5 0.1 0.75765 0.02 0.181818 0.900901 221.2285 0.902669 0.023441


Page 209

Table A. 3 (continued)

Exp Reactor length

D Vr υl υg Volumetric quality, β

Mean RT Void fraction ε

D/uL

cm cm cc cc/min cc/min s 31_10 93.5 0.1 0.75765 0.05 0.167926 0.770564 236.8411 0.7395 0.007572 31_11 93.5 0.1 0.75765 0.1 0.152905 0.604595 206.2997 0.546185 0.003983 31_12 93.5 0.1 0.75765 0.3 0.12945 0.301432 127.6534 0.15757 0.004683 31_13 93.5 0.1 0.75765 0.15 0.142857 0.487805 196.2758 0.352353 0.000542 31_14'' 97.5 0.1 0.790063 0.5 0.162075 0.244798 86.30805 0.08965 0.000965 31_15' 97.5 0.1 0.790063 0.25 0.168209 0.402212 139.9723 0.261808 0.001964 31_16 97.5 0.1 0.790063 0.07 0.136705 0.661354 240.6984 0.644567 0.002236 31_17 97.5 0.1 0.790063 0.03 0.157729 0.840195 190.6332 0.879356 6.82E-05 31_18 97.5 0.1 0.790063 0.13 0.166667 0.561798 194.8267 0.465708 0.000617 36_1 103 0.05 0.208658 0.005 2 0.997506 17.71025 0.992927 1.325351 36_2 103 0.05 0.208658 0.005 0.2 0.97561 76.78833 0.969332 0.227085 36_3 103 0.05 0.208658 0.02 0.2 0.909091 49.8353 0.920387 0.056659 36_4 103 0.05 0.208658 0.05 0.163265 0.76555 66.02941 0.736293 0.003788 36_5 103 0.05 0.208658 0.1 0.151515 0.60241 63.40049 0.493584 0.001963 36_7 103 0.05 0.208658 0.3 0.125 0.294118 34.86917 0.164441 0.006757 36_8 103 0.05 0.208658 0.15 0.132802 0.469594 52.33121 0.373002 0.002984 36_9 103 0.05 0.208658 0.12 0.135135 0.529661 61.55923 0.40995 0.007856 36_6' 103 0.05 0.208658 0.2 0.12987 0.393701 50.38296 0.195126 0.006038 36_10 103 0.05 0.208658 0.06 0.161551 0.729182 60.98144 0.707744 0.020497 36_11 103 0.05 0.208658 0.04 0.166667 0.806452 77.69802 0.751753 0.010799 36_12 103 0.05 0.208658 0.08 0.142857 0.641026 86.82808 0.445164 0.003001 36_14 103 0.05 0.208658 0.25 0.13245 0.34632 38.81996 0.224808 0.001667 36_13' 103 0.05 0.208658 0.18 0.135135 0.428816 50.47935 0.274227 0.001078 38_1 265.8 0.025 0.134615 0.005 0.190658 0.974445 92.63664 0.942653 0.567688 38_3 265.8 0.025 0.134615 0.02 0.181159 0.900576 53.17411 0.86833 0.182469 38_4 265.8 0.025 0.134615 0.05 0.158103 0.759734 44.34948 0.725454 0.069201 38_5 265.8 0.025 0.134615 0.1 0.133333 0.571429 41.38256 0.487641 0.002868 38_6 265.8 0.025 0.134615 0.2 0.096618 0.325733 32.44125 0.196688 0.010978


Page 210

Table A. 4 Experimental data of residence time distribution experiments for N2/pure methanol system.

Exp Reactor length

ID Vr υl υg Volumetric quality, β

Mean RT Void fraction ε

D/uL

cm cm ml ml/min ml/min s 35_1 87 0.1 0.70498 0.005 2 0.99751 355.55 0.95797 0.03746 35_2 87 0.1 0.70498 0.005 0.2 0.97561 249.947 0.97046 0.0216 35_3 87 0.1 0.70498 0.02 0.2 0.90909 124.59 0.94109 0.0068 35_01 87 0.1 0.70498 0.2 0.2 0.5 98.4346 0.53457 0.00457 35_02 87 0.1 0.70498 0.05 0.2 0.8 168.276 0.80109 0.00082 35_03 87 0.1 0.70498 0.1 0.2 0.66667 142.331 0.66351 0.00028 35_04 87 0.1 0.70498 0.15 0.2 0.57143 125.14 0.55623 0.00166 35_05‘ 97.5 0.1 0.79006 0.3 0.1998 0.39976 87.3037 0.44749 7.29E-05 35_06 97.5 0.1 0.79006 0.4 0.19685 0.32982 74.3551 0.37258 0.00061 35_07 97.5 0.1 0.79006 0.6 0.1998 0.24981 56.1025 0.2899 1.36E-05 35_08 97.5 0.1 0.79006 0.8 0.19802 0.19841 46.001 0.22367 0.00025 37_1 103 0.05 0.20866 0.005 2 0.99751 41.8446 0.98329 0.40335 37_2 103 0.05 0.20866 0.005 0.2 0.97561 66.9985 0.97324 0.11202 37_3 103 0.05 0.20866 0.02 0.2 0.90909 52.0701 0.91682 0.05007 37_4 103 0.05 0.20866 0.05 0.2 0.8 49.4608 0.80246 0.01032 37_5 103 0.05 0.20866 0.1 0.2 0.66667 66.6464 0.46766 0.00767 37_6 103 0.05 0.20866 0.2 0.2 0.5 32.7534 0.47676 0.00122 37_7 103 0.05 0.20866 0.3 0.2 0.4 31.529 0.24448 8.46E-05


Page 211

Table A. 5 Experimental data of residence time distribution experiments for N2/10% aqueous glycerol system.

Exp Reactor length

ID Vr υl υg Volumetric quality, β

Mean RT

Void fraction ε

D/uL

cm cm ml ml/min ml/min s 39_1 97.5 0.1 0.79006 0.005 2 0.99751 6.2159 0.99934 1.74945

39_2 97.5 0.1 0.79006 0.005 0.18433 0.97359 217.892 0.97702 0.03246

39_3 97.5 0.1 0.79006 0.02 0.11173 0.84818 210.646 0.91113 0.01453

39_4 97.5 0.1 0.79006 0.05 0.1087 0.68493 305.924 0.67732 0.00114

39_5 97.5 0.1 0.79006 0.1 0.11933 0.54407 208.156 0.56089 3.75E-

05

39_6 97.5 0.1 0.79006 0.2 0.13605 0.40486 138.613 0.41518 0.00039

39_7' 97.5 0.1 0.79006 0.3 0.13072 0.30349 102.612 0.35061 0.00225

39_8 97.5 0.1 0.79006 0.4 0.13289 0.24938 84.9248 0.28339 0.00214

39_9 97.5 0.1 0.79006 0.5 0.13405 0.21142 72.1598 0.23888 0.00309


Page 212

Table A. 6 Predictions of void fraction from previous hydrodynamic models and our suggested correlation for the N2/DI water system.

Exp Volumetric quality

Homogenous Armand Chawla Serizawa Tripplet Coleman Kawahara Kariyasaki Saisorn New correlation

εg εg εg εg εg εg εg εg εg εg

31_4 0.97561 0.97561 0.817374 0.080186 0.758971 0.814182 0.860074 0.707166 0.999875 0.533944 0.974202

31_5 0.990099 0.990099 0.839865 0.068801 0.768968 0.887339 0.914582 0.857448 0.999942 0.600124 0.989602

31_6 0.995025 0.995025 0.85869 0.062262 0.772367 0.924663 0.944518 0.923165 0.999967 0.626121 0.994788

31_7 0.996678 0.996678 0.872192 0.059055 0.773508 0.940864 0.958357 0.94741 0.999977 0.63531 0.996522

31_8 0.997506 0.997506 0.88304 0.057 0.774079 0.950314 0.966684 0.960024 0.999982 0.640009 0.997391

31_9 0.900901 0.900901 0.749405 0.093275 0.707422 0.629294 0.721353 0.359 0.998197 0.331597 0.891374

31_10 0.770564 0.770564 0.639568 0.104295 0.617489 0.472999 0.584502 0.177317 0.989408 0.185387 0.73418

31_11 0.604595 0.604595 0.501814 0.114704 0.50297 0.351673 0.455314 0.094913 0.959419 0.105547 0.517805

31_12 0.301432 0.301432 0.250188 0.134417 0.293788 0.194445 0.245739 0.035236 0.725201 0.041077 0.150828

31_13 0.487805 0.487805 0.404878 0.121749 0.422385 0.28604 0.374032 0.064966 0.912806 0.073955 0.364766

31_14'' 0.244798 0.244798 0.203182 0.135339 0.254711 0.167359 0.20502 0.02854 0.55026 0.033453 0.100298

31_15' 0.402212 0.402212 0.333836 0.124258 0.363326 0.242858 0.315635 0.049441 0.821822 0.056981 0.259421

31_16 0.661354 0.661354 0.548924 0.113053 0.542134 0.38815 0.496809 0.115538 0.97673 0.126469 0.592948

31_17 0.840195 0.840195 0.697362 0.100135 0.665534 0.544563 0.65047 0.24801 0.99568 0.246638 0.820025

31_18 0.561798 0.561798 0.466292 0.115841 0.47344 0.326413 0.425075 0.08238 0.93957 0.092505 0.461131

36_1 0.997506 0.997506 0.88304 0.052644 0.774079 0.950314 0.966684 0.960024 0.999891 0.640009 0.997391

36_2 0.97561 0.97561 0.817374 0.071251 0.758971 0.814182 0.860074 0.707166 0.999264 0.533944 0.974202

36_3 0.909091 0.909091 0.756383 0.080186 0.713073 0.643408 0.732554 0.380668 0.990254 0.346791 0.900729

36_4 0.76555 0.76555 0.635407 0.090924 0.61403 0.468511 0.580141 0.173498 0.939299 0.181898 0.727852

36_5 0.60241 0.60241 0.5 0.099075 0.501463 0.350342 0.453751 0.094218 0.799151 0.104831 0.514906

36_7 0.294118 0.294118 0.244118 0.116163 0.288741 0.190962 0.240556 0.034329 0.302994 0.040049 0.143823

36_8 0.469594 0.469594 0.389763 0.106337 0.40982 0.276597 0.361598 0.061315 0.625594 0.070001 0.341646

36_9 0.529661 0.529661 0.439619 0.103452 0.451266 0.308435 0.402765 0.074249 0.720127 0.083907 0.418904


Page 213

Table A. 6 (continued)


Homogenous Armand Chawla Serizawa Tripplet Coleman Kawahara Kariyasaki Saisorn New correlation

εg εg εg εg εg εg εg εg εg εg 36_6' 0.393701 0.393701 0.326772 0.110215 0.357454 0.238702 0.30981 0.048097 0.489218 0.055492 0.249495

36_10 0.729182 0.729182 0.605221 0.092794 0.588935 0.437931 0.549642 0.149203 0.916021 0.159244 0.681439

36_11 0.806452 0.806452 0.669355 0.088584 0.642252 0.507471 0.617081 0.208982 0.959827 0.213583 0.77892

36_12 0.641026 0.641026 0.532051 0.097995 0.528108 0.374635 0.481723 0.107527 0.851881 0.118421 0.566096

36_14 0.34632 0.34632 0.287446 0.112438 0.324761 0.215848 0.277167 0.041137 0.390768 0.047729 0.196607

36_13' 0.428816 0.428816 0.355918 0.108036 0.381683 0.255985 0.333801 0.053851 0.546583 0.061846 0.29117

38_1 0.974445 0.974445 0.816059 0.064643 0.758167 0.809505 0.856665 0.697226 0.995501 0.529197 0.972955

38_3 0.900576 0.900576 0.74913 0.072399 0.707198 0.628752 0.72092 0.358187 0.940727 0.331019 0.891002

38_4 0.759734 0.759734 0.630579 0.080187 0.610017 0.463394 0.575134 0.169224 0.718705 0.177972 0.720488

38_5 0.571429 0.571429 0.474286 0.088379 0.480086 0.331956 0.43182 0.085016 0.377643 0.095269 0.473856

38_6 0.325733 0.325733 0.270358 0.101242 0.310556 0.206018 0.262828 0.038356 0.112737 0.044602 0.175039


Page 214

Table A. 7 Predictions of void fraction from previous hydrodynamic models and our suggested correlation for the N2/ methanol system.


Homogenous Armand Chawla Serizawa Triplett Coleman Kawahara Kariyasaki Saisorn

εg εg εg εg εg εg εg εg εg

35_1 0.997506 0.997506 0.892428 0.040596 0.774079 0.955067 0.969315 0.960024 0.999966 0.640009

35_2 0.97561 0.97561 0.819348 0.065836 0.758971 0.829621 0.861675 0.707166 0.999772 0.533944

35_3 0.909091 0.909091 0.756881 0.079239 0.713073 0.667237 0.733288 0.380668 0.996959 0.346791

35_01 0.5 0.5 0.415 0.11078 0.4308 0.314764 0.382489 0.067535 0.815588 0.076724

35_02 0.8 0.8 0.664 0.090276 0.6378 0.527295 0.611415 0.202656 0.983359 0.208052

35_03 0.666667 0.666667 0.553333 0.099926 0.5458 0.417189 0.50102 0.117765 0.941746 0.128689

35_04 0.571429 0.571429 0.474286 0.106125 0.480086 0.355758 0.43197 0.085016 0.883366 0.095269

35_05‘ 0.39976 0.39976 0.331801 0.117745 0.361634 0.261521 0.31403 0.049051 0.674298 0.056549

35_06 0.329815 0.329815 0.273747 0.12348 0.313373 0.225882 0.265731 0.038897 0.544228 0.045211

35_07 0.249813 0.249813 0.207344 0.130619 0.258171 0.185172 0.208715 0.029105 0.361584 0.034099

35_08 0.198413 0.198413 0.164683 0.13671 0.222705 0.15822 0.17046 0.02353 0.247146 0.027692

37_1 0.997506 0.997506 0.892428 0.036304 0.774079 0.955067 0.969315 0.960024 0.999801 0.640009

37_2 0.97561 0.97561 0.819348 0.055701 0.758971 0.829621 0.861675 0.707166 0.998656 0.533944

37_3 0.909091 0.909091 0.756881 0.065836 0.713073 0.667237 0.733288 0.380668 0.982331 0.346791

37_4 0.8 0.8 0.664 0.074279 0.6378 0.527295 0.611415 0.202656 0.909262 0.208052

37_5 0.666667 0.666667 0.553333 0.081755 0.5458 0.417189 0.50102 0.117765 0.73272 0.128689

37_6 0.5 0.5 0.415 0.090276 0.4308 0.314764 0.382489 0.067535 0.428562 0.076724

37_7 0.4 0.4 0.332 0.095778 0.3618 0.261645 0.314194 0.049089 0.260006 0.056591


Page 215

Table A. 8 Predictions of void fraction from previous hydrodynamic models and our suggested correlation for the N2/10% aqueous glycerol system.


Homogenous Armand Chawla Serizawa Triplett Coleman Kawahara Kariyasaki Saisorn

εg εg εg εg εg εg εg εg εg

39_1 0.997506 0.997506 0.882158 0.066611 0.774079 0.949182 0.966437 0.960024 0.999976 0.640009

39_2 0.973591 0.973591 0.814954 0.089378 0.757578 0.80242 0.85409 0.690103 0.999826 0.525764

39_3 0.848176 0.848176 0.703986 0.108863 0.671042 0.548312 0.658827 0.259028 0.99649 0.25565

39_4 0.684932 0.684932 0.568493 0.118847 0.558403 0.398863 0.514671 0.125889 0.9804 0.136724

39_5 0.54407 0.54407 0.451578 0.12455 0.461208 0.311295 0.412723 0.077775 0.936656 0.087649

39_6 0.404858 0.404858 0.336032 0.129671 0.365152 0.239805 0.317439 0.049865 0.818527 0.057451

39_7' 0.30349 0.30349 0.251897 0.135738 0.295208 0.191723 0.247191 0.035494 0.671499 0.041369

39_8 0.249377 0.249377 0.206983 0.139047 0.25787 0.166252 0.208364 0.029056 0.547527 0.034043

39_9 0.211416 0.211416 0.175476 0.141782 0.231677 0.148087 0.180265 0.024899 0.44537 0.029272


Page 216

Figure A. 30 Comparison of different hydrodynamic models with experimental void fraction data for a N2/water system in circular PFA capillaries of 0.25, 0.5 and 1mm inner diameter.

Page 217

Appendix D

Validation of RTD Method with Liquid Only Experiments

For the validation of the methodology developed for conducting RTD

experiments, initial experiments were performed only with liquid to get

familiar with this type of experiment and demonstrate the validity of this

methodology. Comparison between the experimentally measured mean time

of the liquid and the theoretically expected one was conducted to validate

the analysis accuracy of this method. It should be noted that each set of

experiments was repeated 2-3 times and the average between the

experiments was considered (the deviation between the runs was ranging

between 0 and 20%). The liquid used was sodium carbonate:bicarbonate

buffer solution (1:9), the same used for the study of the model system.

Liquid Flowrate: 0.03ml/min

In Figure A. 31 the experimental data collected in the outlet of the capillary

forming the F(t) curve is shown where t=0 when the tracer dye reaches the

detector in the inlet of the reactor. Hence, the signal in the inlet of the reactor

was used in order to estimate the time when the tracer dye reaches the

detector in the inlet.

Figure A. 31 F curve against t(s) for the case of 0.3ml/min buffer solution.

Appendix D. Standard Operating Procedure

Page 218

At this point, it should be reminded again that the step change in the inlet of

the reactor was considered to be sharp enough and therefore the convolution

integral was not calculated. After that, the data were fitted as shown in

Figure A. 31 by a trend line (found in Origin database of trend lines) which is

called ‘Boltzmann’ and follows the equation below:

(A. 1)

where , , , are constants.

Then the trend line was differentiated giving the E(t) (E=dF/dt) curve as it is

shown in Figure A. 32.

Figure A. 32 F,E curves against t(s) for the case of 0.3ml/min buffer solution.

The mean residence time was found to be 1375s based on (2.18). The

corresponding hydraulic residence time ( 0h V ) is h =1425s which

means that the deviation of the above experimental results with theory is

only 3.5% indicating that this method for RTD analysis is valid and hence

can be used in multiphase system with confidence.

1 2

2

01 exp

A Ay A

x x

dx

1A 2A 0x dx

Page 219

Appendix E

Vapour-liquid Equilibrium and Reactor Models in gPROMS

1. Vapour-Liquid Equilibrium Model

PARAMETER

no_comp as integer # number of componets [-] 1. methanol / 2.methyl propionate/ 3. carbon monoxide/ 4. ethylene

R as real # gas constant [J/(mol K)]

P_gas_in as real # pressure of gas phase [bar]

temp_in as real # temperature at inlet of set-up [K]

temp_eq as real # temperature at equilibriun (inlet of reactor) [K]

Ug_in, Ul_in as real # gas, liquid volumetric flowrate in the inlet of set-up [ml/min]

x_in, y_in as array(no_comp) of real # concentration in fluid liquid/ gas in the inlet of set-up [mol/mol]

Cl_in as array(no_comp) of real #initial_liquid_concentration

#dens as array(no_comp) of real #concentration of pure components (g/mol)

VARIABLE

x_eq, y_eq as DISTRIBUTION(no_comp) of concentration # concentration at inlet of reactor [mol/mol]

P_vap as DISTRIBUTION(no_comp) of pressure # vapoer pressure of pure components [bar] (Torres thesis, p.257,eq.1.39)

He_MeOH as DISTRIBUTION(no_comp) of Henry_constant # Henry's constant for components that xi<=0.03 (CO, C2H4) in pure MeOH at Pv,j (Torres thesis, p.256,eq.1.33)

He_MeP as DISTRIBUTION(no_comp) of Henry_constant # Henry's constant for components that xi<=0.03 (CO, C2H4) in pure MeP at Pv,j (Torres thesis, p.256,eq.1.33)

He_MeOH_p as DISTRIBUTION(no_comp) of Henry_constant # Henry's constant for components that xi<=0.03 (CO, C2H4) in pure MeOH at elevated pressure-Poynting factor correction (Torres thesis, p.257,eq.1.18)

He_MeP_p as DISTRIBUTION(no_comp) of Henry_constant # Henry's constant for components that xi<=0.03 (CO, C2H4) in pure MeP at elevated pressure-Poynting factor correction (Torres thesis, p.257,eq.1.18)

Appendix E. Vapour-Liquid Equilibrium and Reactor Models in gPROMS

Page 220

He_mix_p as DISTRIBUTION(no_comp) of Henry_constant # Henry's constant for components that xi<=0.03 (CO, C2H4) in MIXTURE at elevated pressure (Torres thesis, p.256,eq.1.31)

Vinf_MeOH as DISTRIBUTION(no_comp) of volume # partial molar volume of dissolved gas in MeOH-needed for the correction of Henry's constatnt at elevated pressure [ml] (Torres thesis, p.258)

Vinf_MeP as DISTRIBUTION(no_comp) of volume # partial molar volume of dissolved gas in MeP-needed for the correction of Henry's constatnt at elevated pressure [ml] (Torres thesis, p.258)

V_0 as DISTRIBUTION(no_comp) of molar_volume # characteristic volume of substance i [ml/mol] (Torres thesis, p.258, Tab.A.7)

c_MeOH as DISTRIBUTION(no_comp) of constant_neg # constant needed for the calculation of partial molar volume [-] (Torres thesis, p.258)

c_MeP as DISTRIBUTION(no_comp) of constant_neg # constant needed for the calculation of partial molar volume [-] (Torres thesis, p.258)

Z as DISTRIBUTION(no_comp) of fugacity_constant_1 # Rackett compressibility factor for pure component, needed for calulation of fugacity in the vapor phase- (based on Torres thesis-p.251, Tab.A.1)

g as DISTRIBUTION(no_comp) of activity_coefficient # activity coefficient

phi as DISTRIBUTION(no_comp) of activity_constant # constant needed for calculation of activity

q as DISTRIBUTION(no_comp) of activity_constant # constant needed for calculation of activity

theta as DISTRIBUTION(no_comp) of activity_constant # constant needed for calculation of activity

lu as DISTRIBUTION(no_comp) of activity_constant_neg # constant needed for calculation of activity

tau as DISTRIBUTION(no_comp,no_comp) of activity_constant # constant needed for calculation of activity

aa as DISTRIBUTION(no_comp,no_comp) of activity_constant_neg # constant needed for calculation of activity

bb as DISTRIBUTION(no_comp,no_comp) of activity_constant_neg # constant needed for calculation of activity

ro as DISTRIBUTION(no_comp) of activity_constant # constant needed for calculation of activity

ro_total as activity_constant # constant needed for calculation of activity

q_total as activity_constant # constant needed for calculation of activity

sum as DISTRIBUTION(no_comp) of activity_constant # parameter used to simplify activity expression


Page 221

phi_v as DISTRIBUTION(no_comp) of fugacity # fugacity of component i (based on Torres thesis, p.254, eq.A.2)

bbb as DISTRIBUTION(no_comp) of fugacity_constant # parameter b for pure component needed for calculation of fugacity in the vapor phase- (based on Torres thesis-p.250, eq.1.23)

aaa as DISTRIBUTION(no_comp) of fugacity_constant # parameter b for pure component needed for calculation of fugacity in the vapor phase- (based on Torres thesis-p.250, eq.1.23)

bbb_mix as fugacity_constant # parameter b for mixture needed for calculation of fugacity in the vapor phase- (based on Torres thesis-p.250, eq.1.24)

aaa_mix as fugacity_constant # parameter b for mixture needed for calculation of fugacity in the vapor phase- (based on Torres thesis-p.250, eq.1.23)

Tc as DISTRIBUTION(no_comp) of fugacity_constant # critical temperature of component i [K], needed for calulation of fugacity in the vapor phase- (based on Torres thesis-p.251, Tab.A.1)

Pc as DISTRIBUTION(no_comp) of fugacity_constant # critical pressure of component i [bar], needed for calulation of fugacity in the vapor phase- (based on Torres thesis-p.251, Tab.A.1)

Tr as DISTRIBUTION(no_comp) of fugacity_constant_1 # dimensionless critical temperature of component i [-],Tr=T/Tc ,needed for calulation of fugacity in the vapor phase

Vav as DISTRIBUTION(no_comp) of fugacity_constant_1 # pure component saturated volume - needed for calculation of fugacity in the vapor phase- (based on Torres thesis-p.250, eq.1.36) [ml]

Fg_eq, Fl_eq as molar_flowrate # gas, liquid molar flowrate in the equilibrium (inlet of reactor) [mol/min]

Fg_in,Fl_in as molar_flowrate # gas, liquid molar flowrate in the inlet of set-up [mol/min]

Ug_eq, Ul_eq as volumetric_flowrate # gas, liquid volumetric flowrate in the equilibrium (inlet of reactor) [ml/min]

p_av_MeOH,p_av_MeP as density # density of pure MeOH, MeP reduced by its characteristic volume [-] (Torres thesis, p.258)

p_MeOH,p_MeP as density # density of pure MeOH, MeP [mol/ml] (Torres thesis, p.258,eq.1.37)

dens_mix as density #density of the MeOH:MeP mixture in equilibrium [mol/m l]

EQUATION

#general expression for VLE


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y_eq(1)*phi_v(1)*P_gas_in =g(1)*x_eq(1)*P_vap(1) ;

y_eq(2)*phi_v(2)*P_gas_in =g(2)*x_eq(2)*P_vap(2) ;

y_eq(3)*phi_v(3)*P_gas_in =g(3)*x_eq(3)*He_mix_p(3) ; # Henry's law can be used only for very small conentrations of the component in the colution.

y_eq(4)*phi_v(4)*P_gas_in =g(4)*x_eq(4)*He_mix_p(4) ; # Therefore, it's valid only for CO and C2H4

FOR i:=1 TO no_comp DO

(x_eq(i)*Fl_eq)+(y_eq(i)*Fg_eq)=(Ul_in*Cl_in(i))+(y_in(i)*Fg_in); # mass balance for each component

END

Sigma(x_eq) = 1;

Sigma(y_eq) = 1;

Ug_eq=Fg_eq*R*temp_eq/P_gas_in; # calculation of volumetric flowrate of the gas and the liquid phase in the inlet

dens_mix=x_eq(1)*p_MeOH+x_eq(2)*p_MeP; #calculation of density of the MeOH:MeP mixture in equilibrium - needed for the calculation of Ul in equilibrium

Ul_eq=Fl_eq*dens_mix ; #calculation of liquid volumetric flowrate in equilibrium

# calculation of inlet molar flowrates in gas and in liquid phase

Fl_in=Ul_in*Cl_in(1)+Ul_in*Cl_in(2) ; # total lquid molar flowrate in the inlet(mol/min)

Fg_in=(P_gas_in*Ug_in/(R*temp_in)); # total gas molar flowrate in the inlet(mol/min)

#calculation of phi_v which is the fugacity coefficient of the vapor phase

Vav(1)=R*Tc(1)*(Z(1)^((1+((1-Tr(1))^(2/7)))))/Pc(1) ;

Vav(2)=R*Tc(2)*(Z(2)^((1+((1-Tr(2))^(2/7)))))/Pc(2) ;

Vav(3)=R*Tc(3)*(Z(3)^((1+((-1+Tr(3))^(2/7)))))/Pc(3) ; #modified as for CO,C2H4 (1-Tr)<0 and a negative number cannot be at a not integer power (2/7)_ I checked even with getting rid of this part (1-Tr=1)

and the results remain the same. So this change does not impact the final results of the VLE.

Vav(4)=R*Tc(4)*(Z(4)^((1+((-1+Tr(4))^(2/7)))))/Pc(4) ; #modified -//-

SQRT(aaa_mix)=SIGMA(y_eq()*(SQRT(aaa()))) ;

bbb_mix=SIGMA(y_eq()*bbb()) ;

Tc(1)=512.64 ; Tc(2)=530.6 ; Tc(3)=132.92 ; Tc(4)=282.34;

Pc(1)=80.97 ; Pc(2)=40.04 ; Pc(3)=34.987 ; Pc(4)=50.4;


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Z(1)=0.2353 ; Z(2)=0.2566 ;

Z(3)=0.2896 ; Z(4)=0.2808;


log(phi_v(i))=log(Vav(i)/(Vav(i)-bbb_mix))+(((2*bbb_mix*SQRT(aaa_mix)*SQRT(aaa(i)))+R*temp_eq*aaa_mix*bbb(i))*(log(Vav(i)/(Vav(i)+bbb_mix)))/(R*temp_eq*(bbb_mix^2)))+(bbb(i)/(Vav(i)-bbb_mix))+((aaa_mix*bbb(i))/(bbb_mix*(Vav(i)+bbb_mix))) ;

aaa(i)=(0.42748*(0.08314^2)*(Tc(i)^2.5))/(Pc(i)); #*(temp_eq)^0.5) ;

bbb(i)=(0.08664*0.08314*Tc(i))/Pc(i) ;

Tr(i)=temp_eq/Tc(i);

END

# UNIQUAC equation: calculation of g(i) which is the activity coefficient of component i


log(g(i))=(log((phi(i)/x_eq(i))))+(5*q(i)*(log(theta(i)/phi(i))))+lu(i)-((phi(i)/x_eq(i))*(SIGMA(x_eq()*lu())))+(q(i)*((1-(log(SIGMA(theta()*tau(,i))))-(SIGMA((theta()*tau(i,))/sum()))))) ;

FOR j:=1 TO no_comp DO

tau(i,j)=(exp(aa(i,j)+(bb(i,j)/temp_eq))) ;

END

END

FOR k:=1 TO no_comp DO

sum(k)=SIGMA(theta*tau(,k));

END

#calculation of components properties needed for the resolution of UNIQUAC equation( for the calculation of activity coefficient,g(i))

phi()=ro()*x_eq()/ro_total ;

theta()=q()*x_eq()/q_total ;

lu()=(5*(ro()-q()))+1-ro() ;

ro_total=(SIGMA(ro()*x_eq())) ;

q_total=(SIGMA(q()*x_eq())) ;

ro(1)=1.43111; ro(2)=3.47858; ro(3)=1.0679; ro(4)=1.57416;

q(1)=1.432; q(2)=3.116; q(3)=1.112; q(4)=1.488;

aa(1,1)=0; aa(1,2)=0.29199; aa(1,3)=0; aa(1,4)=0;

aa(2,1)=0.010522; aa(2,2)=0; aa(2,3)=0; aa(2,4)=0;


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aa(3,1)=0; aa(3,2)=0; aa(3,3)=0; aa(3,4)=0;

aa(4,1)=0; aa(4,2)=0; aa(4,3)=0; aa(4,4)=0;

bb(1,1)=0; bb(1,2)=-408.75; bb(1,3)=0; bb(1,4)=-13023.2;

bb(2,1)=22.382; bb(2,2)=0; bb(2,3)=0; bb(2,4)=0;

bb(3,1)=0; bb(3,2)=0; bb(3,3)=0; bb(3,4)=0;

bb(4,1)=-144.865; bb(4,2)=0; bb(4,3)=0; bb(4,4)=0;

# calculation of vapor pressures of component i (MeOH, MeP, CO, C2H4) using Antoine equation

# constants based on Torres thesis (p.257, Tab.A.6)

P_vap(1) =10^(-5)*exp(81.768+(-6876/(temp_eq))+(-8.7078*log(temp_eq))+(7.1926E-06*(temp_eq^2))); # P_vap [bar] T [K]

P_vap(2) =10^(-5)*exp(70.717+(-6439.7/(temp_eq))+(-6.9845*log(temp_eq))+(2.0129E-17*(temp_eq^6))) ; # P_vap [bar] T [K]

P_vap(3) =0 ; # we need to set the zero value because P_vap is defined as 4component row but we are not interested in P-vap of CO,C2H4

P_vap(4) =0 ; # same

#Henry's constant for components i where xi<=0.03 (CO, C2H4) in the mixture MeOH:MeP at elevated pressure

# Henry's constant of components i at pure MeOH, MeP at vapor pressure (p.256, eq.1.33, Tab.A.5)

He_MeOH(1)=0 ; # we need to set the zero value because He_MeOH is defined as 4component row but we are not interested in He of MeOH, MeP

He_MeOH(2)=0 ; # same

He_MeP(1)=0 ; # same

He_MeP(2)=0 ; # same

#calculation of He of CO in MeOH at T, Pv,j based on Torres thesis (p.256, eq.1.33, Tab.A.5)

He_MeOH(3)=10^(-5)*EXP(86.9474+(-3113.31/temp_eq)+(-10.0276*(log(temp_eq)))); # He [bar], temp_eq [K]

#calculation of He of CO in MeP at T, Pv,j based on Torres thesis (p.256, eq.1.33, Tab.A.5)

He_MeP(3)=10^(-5)*EXP(16.7289+(509.750/temp_eq));

#calculation of He of C2H4 in MeOH at T, Pv,j based on Torres thesis (p.256, eq.1.33, Tab.A.5)

He_MeOH(4)=10^(-5)*EXP(20.6312+(-1054.03/temp_eq));

#calculation of He of C2H4 in MeP at T, Pv,j based on Torres thesis (p.256, eq.1.33, Tab.A.5)


Page 225

He_MeP(4)=10^(-5)*EXP(15.4734+(-719.82/temp_eq)+(0.15527*(log(temp_eq)))+(0.005046*(temp_eq)));

# Henry's constant of components i at pure MeOH, MeP at elevated pressure- correction by the Poynting factor

He_MeOH_p(1)=0 ; # we need to set the zero value because He_MeOH_p is defined as 4component row but we are not interested in He of MeOH (only for CO,C2H4)

He_MeOH_p(2)=0 ; # same

He_MeP_p(1)=0 ; # we need to set the zero value because He_MeP_p is defined as 4component row but we are not interested in He of MeP (only for CO,C2H4)

He_MeP_p(2)=0 ; # same

#calculation of He of CO in MeOH at T, elevated P based on Torres thesis (p.257, eq.1.18)

log(He_MeOH_p(3))=log(He_MeOH(3))+(Vinf_MeOH(3)*(P_gas_in-P_vap(1))/(R*temp_eq)); # we multiply Vinf with 10-2 to convert m3 Pa/kmol to ml bar/mol

#calculation of He of CO in MeP at T, elevated P based on Torres thesis (p.257, eq.1.18)

log(He_MeP_p(3))=log(He_MeP(3))+(Vinf_MeP(3)*(P_gas_in-P_vap(2))/(R*temp_eq));

#calculation of He of C2H4 in MeOH at T, elevated P based on Torres thesis (p.257, eq.1.18)

log(He_MeOH_p(4))=log(He_MeOH(4))+(Vinf_MeOH(4)*(P_gas_in-P_vap(1))/(R*temp_eq));

#calculation of He of C2H4 in MeP at T, elevated P based on Torres thesis (p.257, eq.1.18)

log(He_MeP_p(4))=log(He_MeP(4))+(Vinf_MeP(4)*(P_gas_in-P_vap(2))/(R*temp_eq));

#calculation of partial molar volume of i at infinite dilution in pure solvent j (Vinf_j(i) - needed for the correction of He at elevated pressure (Torres thesis,p.258)

Vinf_MeOH(1)=0 ; Vinf_MeOH(2)=0 ; # we need to set the zero value because Vinf_MeOH is defined as 4component row but we are not interested in He of MeOH (only for CO,C2H4)

Vinf_MeP(1)=0 ; Vinf_Mep(2)=0 ; # we need to set the zero value because Vinf_MeP is defined as 4component row but we are not interested in He of MeP (only for CO,C2H4)

#of dissolved CO in MeOH (Vinf_MeOH(3))

Vinf_MeOH(3)/(Z(1)*0.008314*temp_eq)=1-c_MeOH(3); #Vinf [m3 Pa/kmol],Z[-], 0.008314 [m3 Pa/kmol K], temp_eq [K]

#of dissolved CO in MeP (Vinf_MeP(3))

Vinf_MeP(3)/(Z(2)*0.008314*temp_eq)=1-c_MeP(3);

#of dissolved C2H4 in MeOH (Vinf_MeOH(4))

Vinf_MeOH(4)/(Z(1)*0.008314*temp_eq)=1-c_MeOH(4);

#of dissolved C2H4 in MeP (Vinf_MeP(4))


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Vinf_MeP(4)/(Z(2)*0.008314*temp_eq)=1-c_MeP(4);

#calculation of constant c_j(i)-needed for the calculation of partial molar volume V_inf_j(i)(Torres thesis, p.258)

FOR qq:=no_comp-1 TO no_comp DO # this was done because we are interested only on CO,C2H4 for Henry's constants

#calculation of c_MeOH(i)

IF p_av_MeOH<=2.785 THEN

log((-c_MeOH(qq))*((V_0(1)/V_0(qq))^0.62))=-2.4467+(2.12074*p_av_MeOH);

ELSE

log((-c_MeOH(qq))*((V_0(1)/V_0(qq))^0.62))=3.012214-(1.87085*p_av_MeOH)+(0.71955*(p_av_MeOH^2));

END

#calculation of c_Mep(i)

IF p_av_MeP<=2.785 THEN

log((-c_MeP(qq))*((V_0(2)/V_0(qq))^0.68))=-2.4467+(2.12074*p_av_MeP);

ELSE

log((-c_MeP(qq))*((V_0(2)/V_0(qq))^0.68))=3.012214-(1.87085*p_av_MeP)+(0.71955*(p_av_MeP^2));

END

END

V_0(1)= 117.916; # characteristic volume of MeOH [ml/mol] based on Torres thesis, p.258, Tab.A.7 - needed for calculation of c_j(i)

V_0(2)=282; # characteristic volume of MeP [ml/mol] based on Torres thesis, p.258, Tab.A.7 - needed for calculation of c_j(i)

V_0(3)=93.2441; # characteristic volume of CO [ml/mol] based on Torres thesis, p.258, Tab.A.7 - needed for calculation of c_j(i)

V_0(4)=128.68; # characteristic volume of C2H4 [ml/mol] based on Torres thesis, p.258, Tab.A.7 - needed for calculation of c_j(i)

c_MeOH(1)=0 ; c_MeOH(2)=0 ; # we need to set the zero value because c_MeOH is defined as 4component row but we are not interested in He of MeOH (only for CO,C2H4)

c_MeP(1)=0 ; c_Mep(2)=0 ; # we need to set the zero value because c_MeP is defined as 4component row but we are not interested in He of MeP (only for CO,C2H4)

#calculation of p_av_MeOH which is the pure MeOH liquid density reduced by its characteristic volume V_0_MeOH - needed for calculation of c_j(i) - [dimensionless] -based on Torres thesis (p.258)


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p_av_MeOH=p_MeOH*V_0(1);

#calculation of p_av_MeP which is the pure MeP liquid density reduced by its characteristic volume V_0_MeP - needed for calculation of c_j(i) - [dimensionless] -based on Torres thesis (p.258)

p_av_MeP=p_MeP*V_0(2);

#calculation of p_MeOH which is the liquid density of pure MeOH - needed for p_av_MeOH caluclation -[mol/ml] -based on Torres thesis (p.258,eq.1.37)

p_MeOH=0.001*(2.288/(0.2685^(1+((1-(temp_eq/512.64))^0.2453))));

#calculation of p_MeP which is the liquid density of pure MeOH - needed for p_av_MeP caluclation -[mol/ml] -based on Torres thesis (p.258,eq.1.37)

p_MeP=0.001*(0.9147/(0.2594^(1+((1-(temp_eq/530.6))^0.2774))));

# Henry's constant of components i at MeOH, MeP mixtures at elevated pressure(p.256, eq.1.33, Tab.A.5)

He_mix_p(1)=0; # we need to set the zero value because He_mix_p is defined as 4component row but we are not interested in He of MeOH (only for CO,C2H4)

He_mix_p(2)=0; # we need to set the zero value because He_mix_p is defined as 4component row but we are not interested in He of MeP (only for CO,C2H4)

#for CO:

log(He_mix_p(3))=(x_eq(1)*log(He_MeOH_p(3))+x_eq(2)*log(He_MeP_p(3)))/(x_eq(1)+x_eq(2));#based on eq.5.60,p.267, 'Chem. Therm. for Process Simulation',J.Gmehling

#for C2H4:

log(He_mix_p(4))=(x_eq(1)*log(He_MeOH_p(4))+x_eq(2)*log(He_MeP_p(4)))/(x_eq(1)+x_eq(2));

2. Reactor Model

PARAMETER

no_comp AS Integer # Number of components in rxn

dt AS Real # Tubing inner diameter (cm)

Length AS Real # Length of the reactor (cm)

Ug AS Real # Gas volumetric flowrate (ml/min)

Ul AS Real # Liquid volumetric flowrate (ml/min)

A AS Real # Void fraction prefactor; determined from RTD experiments

kla AS Real # Mass transfer coefficient (min-1); determined from correlations. Its value shouldn't affect the results significantly as it is a kinetically controlled system


Page 228

kr AS REAL # reaction rate constant (min-1)

pi AS Real # constant

R AS Real # gas constant (ml bar/mol K)

T AS Real # temperature (K)

P AS Real # pressure (bar)

j AS ARRAY(no_comp) OF Real # prefactor that indicates if a component is a reactant or a product (-)

K AS ARRAY(no_comp) OF Real # gas-liquid interface equilibrium constant, related to Henry's constant (for CO, C2H4) and to vapor pressure (for MeOH, MeP) (-)

DISTRIBUTION_DOMAIN

Axial AS [0:Length] # Axial domain

VARIABLE

Cg AS DISTRIBUTION(Axial, no_comp) OF Concentration # concentration of components (MeOH, MeP, CO, C2H4) in gas phase (mol/ml)

Cl AS DISTRIBUTION(Axial, no_comp) OF Concentration # concentration of components (MeOH, MeP, CO, C2H4) in liquid phase (mol/ml)

Fg AS DISTRIBUTION(Axial, no_comp) OF MolarFlowrate # molar flowrate of components (MeOH, MeP, CO, C2H4) in the gas phase (mol/min)

Fl AS DISTRIBUTION(Axial, no_comp) OF MolarFlowrate # molar flowrate of components (MeOH, MeP, CO, C2H4) in the liquid phase (mol/min)

mol_dif AS DISTRIBUTION(Axial, no_comp) OF MolarFlowrate # mole difference of all componenets between the inlet and the outlet of the reactor to check that the balances are correct (mol/min)

Xrxn AS DISTRIBUTION(Axial, no_comp) OF MolarFlowrate # Conversion of reactants between the inlet and the outlet (-)

x AS DISTRIBUTION(Axial, no_comp) OF Fraction # fraction of component in the liquid phase (-)

y AS DISTRIBUTION(Axial, no_comp) OF Fraction # fraction of component in the gas phase (-)

Fg_total AS DISTRIBUTION(Axial) OF MolarFlowrate # total molar flowrate in the gas phase (mol/min)

Fl_total AS DISTRIBUTION(Axial) OF MolarFlowrate # total molar flowrate in the liquid phase (mol/min)

rxn AS DISTRIBUTION(Axial) OF Concentration # reaction rate expression

e AS NoType # liquid volume fraction

jg AS NoType # gas superficial velocity (cm/min)


Page 229

jl AS NoType # liquid superficial velocity (cm/min)

Ac AS NoType # interfacial contact area (cm^2)

BOUNDARY

Fl(0,1)=5.1261875E-5; # Concentration of MeOH in the liquid phase in the inlet of the reactor (point 2).

Fl(0,2)=4.732016E-5; # Concentration of MeP in the liquid phase in the inlet of the reactor (point 2).

Fl(0,3)=4.7264077E-8; # Concentration of CO in the liquid phase in the inlet of the reactor (point 2).

Fl(0,4)=6.0849015E-7; # Concentration of C2H4 in the liquid phase in the inlet of the reactor(point 2).

Fg(0,1)=2.8710325E-5; # Concentration of MeOH in the gas phase in the inlet of the reactor(point 2).

Fg(0,2)=1.1307638E-5; # Concentration of MeP in the gas phase in the inlet of the reactor(point 2).

Fg(0,3)=8.144223E-6; # Concentration of CO in the gas phase in the inlet of the reactor(point 2)

Fg(0,4)=6.9556976E-5; # Concentration of C2H4 in the gas phase in the inlet of the reactor(point 2).

EQUATION

FOR z:=0|+ TO Length DO

# Mole balances for all components in the gas and the liquid phase along the reactor based on molar flowrates. Flowrate change is not taken into account.

FOR q:=1 TO no_comp DO

(1/Ac)*(PARTIAL(Fl(z,q),Axial))=(j(q)*rxn(z)*e)+(kla*((Fg(z,q)/(Ug*K(q)))-(Fl(z,q)/Ul))) ; # liquid phase

(1/Ac)*(PARTIAL(Fg(z,q),Axial))=-(kla*((Fg(z,q)/(Ug*K(q)))-(Fl(z,q)/Ul))) ; # gas phase

END

END

FOR z:=0 TO Length DO

Fl_total(z)=SIGMA(Fl(z,));

Fg_total(z)=SIGMA(Fg(z,));

rxn(z)=kr*Fl(z,1)/Ul ; # reaction rate expression

FOR q:=1 TO no_comp DO

Cg(z,q)=Fg(z,q)/Ug ; # concentration of gas components

Cl(z,q)=Fl(z,q)/Ul ; # concentration of liquid components

mol_dif(z,q)=((Fg(0,q)+Fl(0,q))-(Fg(z,q)+Fl(z,q))) ; # mole difference of all componenets between the inlet and the outlet of the reactor to check that the balances are correct


Page 230

Xrxn(z,q)=mol_dif(z,q)/(Fg(0,q)+Fl(0,q));

x(z,q)=Fl(z,q)/Fl_total(z) ;

y(z,q)=Fg(z,q)/Fg_total(z) ;

END

END

Ac=pi*(dt^2)/4 ; # interfacial contact area (cm^2)

e=1-(A*(jg/(jg+jl))) ; # liquid volume fraction

jg=Ug/Ac ; # gas superficial velocity (cm/s)

jl=Ul/Ac ; # liquid superficial velocity (cm/s)

Page 231

Appendix F

Fourier number calculation

The dimensionless Fourier number, Fo, number is given by eq.(A.2),

(A.2)

where D(cm2/s) is the diffusion coefficient of MeOH in MeP in our case, t(s)

is the contact time between the gas and the liquid and d(cm) is the diffusion

path length of the liquid which in our case is equal with the film thickness

(≈30μm).

The diffusion coefficient of MeOH in MeP was calculated at 20oC using

Wilke and Chang correlation eq.(A.3) [204] and was found equal with 2.06

10-5 cm2/s.

(A.3)

where x is the association parameter which in the case of MeOH is equal

with 1.9, M(g/ml) is the molecular weight of MeOH, T(K) is the temperature,

n(cP) is the viscosity of the solution and V(ml/mol) is the molar volume of

MeP at normal boiling point.

Hence, in order to achieve equilibrium at the gas-liquid interphase, no more

than a minute is needed. Therefore, it can be concluded that equilibrium is

achieved instantly in the reactor’s inlet considering a typical total residence

time of approximately 40min.

2

D tFo

d

1/2

8

0.67.4 10

x M TD

n V

Page 232

Appendix G

Mass Balance Calculations during Blank Experiment

The mass balance of MeOH was developed for the case of a typical blank

experiment to demonstrate the accuracy of the methodology followed for the

kinetic study of the MeP system. The initial conditions are listed in Table A.

9. In the inlet a 10%CO:C2H4 gas stream and a 30:70w/w% MeOH: MeP

liquid stream (without catalyst in) were introduced.

Table A. 9 Operating conditions of blank experiment

T(K) P(bara) υg (ml/min) υℓ (ml/min)

373 10 2 0.005

Based on the analysis of the gas and the liquid samples, the composition in

the gas and the liquid phase were determined in the set-up feed and outlet as

shown in Table A. 10. Then, the composition in the inlet and outlet of the

reactor (where temperature increases to 100oC) was calculated by means of

the experimental data (in the feed and outlet of the set-up at 25oC) and a VLE

model.

Table A. 10 Gas and liquid compositions in the set-up feed and outlet (as measured experimentally) and in the reactor’s inlet and outlet (as calculated

by means of the VLE model).

Set-up Feed (Experimental Data)

Reactor’s Inlet (VLE predictions)

Set-up Outlet (Experimental Data)

Reactor’s Outlet (VLE predictions)

yi xi yi xi yi xi yi xi

MeOH 0 0.535 0.227 0.466 0.018 0.524 0.226 0.463

MeP 0 0.465 0.102 0.519 0.009 0.464 0.102 0.521

CO 0.098 0 0.069 4.95E-04 0.102 0 0.071 5.14E-04

C2H4 0.872 0 0.603 0.015 0.850 0 0.601 0.015

Appendix G. Mass Balance Calculations during Blank Experiment

Page 233

Then, by using equations (A.4) and (A.5), the molar flowrates of all

components in both the gas and the liquid phase were calculated in all points

of the set-up and most importantly in the inlet and outlet of the reactor. The

results are presented in Table A. 11.

𝐹𝑔 =

𝜐𝑔𝑃

𝑅𝑇 (A.4)

𝐹ℓ = 𝐹ℓ,𝑀𝑒𝑂𝐻 + 𝐹ℓ,𝑀𝑒𝑃=𝜐ℓ𝐶𝑀𝑒𝑂𝐻+𝜐ℓ𝐶𝑀𝑒𝑃 (A.5)

Table A. 11 Molar flowrates of all components in the gas and the liquid phase in the set-up feed and outlet and in the reactor’s inlet and outlet.

Set-up Feed Reactor’s Inlet Set-up Outlet

Reactor’s Outlet

Fgi Fℓi Fgi Fℓi Fgi Fℓi Fgi Fℓi

MeOH 0 7.07E-05

2.59E-05

4.47E-05

1.42E-06

6.92E-05

2.59E-05

4.47E-05

MeP 0 6.14E-05

1.16E-05

4.98E-05

7.42E-07

6.12E-05

1.17E-05

5.03E-05

CO 7.91E-06

0 7.86E-06

4.75E-08

8.22E-06

0 8.17E-06

4.96E-08

C2H4 7.04E-05

0 6.90E-05

1.41E-06

6.86E-05

1.72E-06

6.89E-05

1.42E-06

The error between the molar flowrates in the inlet and the outlet of the

reactor is calculated and is shown in Table A. 12.

Table A. 12 Error% on total molar flowrates of all components between the inlet and outlet of the reactor.

Error %

Ftotal

MeOH 0.13% MeP -0.90% CO -3.88% C2H4 0.14%

The % error in molar flowrates between the inlet and outlet of the reactor is

very small for all components and can be attributed to experimental error of

gc. Error of carbon monoxide is slightly larger because its actual molar

flowrates are of an order of magnitude smaller than the other components.

Hence, it can be concluded that the analysis methods used are valid and the

set-up is suitable for the kinetic study of MeP system with good accuracy.

Page 234

Appendix H

Fabrication of microseparators

Microfabrication of the microseparators used was carried out by a

designated member of the group at the London Centre of Nanotechnology.

A typical procedure involved spin coating a positive photoresist on a clean

silicon wafer creating a 6μm thick layer. The exposed photoresist was then

removed using a developer solution. The patterned wafer was then dry

etched using deep reactive ion etching to the desired depth.

The etched wafer was bonded by the author. More specifically, a solution of

hydrogen peroxide (H2O2) and sulphuric acid (H2SO4) (1:1) was prepared

where the silicon wafers and the glasses were submerged for 20 min at 120oC

in order to clean them. For bonding the silicon wafer to the glass, the two

were carefully aligned inside the anodic bonder. Following this, they were

heated at 400-450oC and then gradually the voltage was increased up to 1kV.

Figure A. 33 Photographs of the glass-silicon microseparator before (left) and after (right) the place of the fittings.

The bottom fittings (Presearch, adhesive ring, PEEK bottom port and gasket)

were centred and placed on the surface of the microseparator, they were

clamped and they were put in the oven at 165-177oC for one hour to develop

a complete bond between the port and the substrate. It should be also noted

that the unused adhesive rings should be stored in a refrigerated

environment (1.7-4.4oC) to ensure maximum usable lifetime.

Page 235

Appendix I

Flow Observation

Figure A. 34 Typical image of flow observation of gas-liquid flow of the model system into a glass circular capillary with ID=1mm by means of a microscope for gas

(2% CO2) and liquid (buffer solution) flowrates 0.3ml/min and 0.03ml/min respectively.

Figure A. 35 Typical image of flow observation of gas-liquid flow of the model

system into a glass circular capillary with ID=1mm by means of a microscope for gas (2% CO2) and liquid (buffer solution) flowrates 0.5ml/min and 0.03ml/min

respectively.

Film thickness

Slug length

Appendix I. Flow Observation

Page 236

Figure A. 36 Typical image of flow observation of gas-liquid flow of the model

system into a glass circular capillary with ID=1mm by means of a microscope for gas (2% CO2) and liquid (buffer solution) flowrates 1ml/min and 0.03ml/min

respectively.

Figure A. 37 Typical image of flow observation of gas-liquid flow of the model system into a glass circular tubing with ID=1mm by means of a microscope for gas

(2% CO2) and liquid (buffer solution) flowrates 2ml/min and 0.03ml/min respectively.

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Appendix J

Supplementary technical data for Chapter 5

1. Standard operating procedure

A standard procedure to start an experiment for the system of the MeP

reaction system was developed for safety and reproducibility reasons and

consists of the following steps:

o Prepare the catalyst mixture under Argon atmosphere (using a glove

box) using degased pure methanol and methyl propionate solutions

to adjust the concentration. The prepared liquid mixture that contains

the catalyst solution should be always consumed within 2days to

avoid catalyst degradation.

o Fill the syringe with the liquid mixture, install it in the syringe pump

and collect initial liquid samples for analysis.

o Open He cylinder, set the desired He flowrate value in the He MFC

and pressurise the set-up at 12bar by means of a BPR.

o Stop the He flow and test for leaks by monitoring the pressure loss

after 10min.After ensuring that there are not any significant leaks,

start He again.

o Open gas CO, C2H4 cylinders (first open the main valve of the

cylinder, set the desired outlet pressure and then open the switch-off

valve of the gas line).

o Set the desired CO, C2H4 flowrates value in the MFC’s and start the

gases.

o Wait until the system is pressurised at 10bara and ensure the gas

composition is the desired one with gc analysis of the gas stream

o Set the desired liquid flowrate and start the liquid.

o Switch on the temperature controller.

Appendix J. Supplementary technical data for Chapter 5

Page 238

o After 20min empty the bottom of the separator of any liquid

remained from the previous set of experiment.

o Wait 3-4 residence times for the system to reach steady state.

o Take liquid samples every 30min by gradually opening the metering

valve in the end of the separator. Liquid samples will be analysed off-

line after the end of the experiment.

o Gas analysis is happening online

o Measure gas flowrate leaving the separator by means of a bubble

meter installed after the reactor

o Before stopping the experiment, inject methanol tracer to perform

RTD experiment and monitor the tracer concentration in the inlet and

the outlet of the reactor. When all the tracer has left the set-up all the

data needed for the RTD experiment has been collected and we can

stop the experiment

To stop the experiment with the MeP system, the next steps need to be

followed:

o Switch off the temperature controller

o Stop the liquid

o Switch off the CO, C2H4 cylinders (first the switch off valve and then

the main cylinder valve)

o Depressurise the set-up (from the main gas lines to the BPR)

gradually

o Switch off CO, C2H4 MFC’s

Purge the set-up with He for 15min overnight to get rid of any left impurities

in the set-up.


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2. Safety precautions

Due to the poisonous nature of carbon monoxide, the flammable nature of

ethylene and the elevated temperature and pressure conditions, safety

precautions were taken before the installation of the new gas cylinders.

The gas lines that connect the gas cylinders with the main set-up were leak

tested by pressurising the lines with helium at 12bara and no leaks were

found. Moreover, the set-up was enclosed in a ventilated acrylic box and a

valve system allowed the flashing with N2 of the lines between the CO

cylinder and the set-up. In this way, potential exposure to CO was

minimised.

In addition, a pressure relief valve that opens when pressure is larger than

17bar was installed in the CO line of the set-up (Figure 5.1) to prevent any

dangerous pressure build up.

The lab was equipped with detectors for carbon monoxide and ethylene that

set off alarms when the gas levels exceeded the corresponding established

European limits (EH 40 Workplace Exposure Limit LEL for carbon

monoxide: 30ppm). An additional carbon monoxide handheld detector was

also placed next to the set-up, inside the ventilated acrylic box for a quicker

response time.


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3. Gas phase analysis

For the gas analysis a polar capillary column (HP-Plot Q, Agilent) and a TCD

detector were used. The developed method for the analysis of CO/C2H4

mixtures is shown in Table A. 13.

Table A. 13 GC operating conditions for the analysis of the gas effluent from the methoxycarbonylation of ethylene.

Column Name HP-PLOT Q

Split Flow 20:1

Column Flow 2ml/min

Oven Temperature

70oC (3min hold)

Ramp 50oC/min to 110oC (1min hold)

Ramp 20oC/min to 200oC (2min hold)

Carrier Gas Helium

Carrier Flowrate 5ml/min

Detector TCD

Filament Temperature 250oC

Make-up Flowrate 5ml/min

Reference Flowrate 20ml/min

Front Signal Frequency 10Hz/0.02min

A typical chromatograph of the analysis of CO, C2H4 in the gas phase is

shown in Figure A. 38 and the total analysis time was ca. 11min.

Figure A. 38 Typical chromatograph of the gas analysis of a 10%v/v CO:C2H4 mixture.

The reproducibility of GC for gas samples was satisfactorily as the relative

standard deviation was calculated to be less than 0.5%. The calibrations for

CO

C2H4


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carbon monoxide and ethylene can be found in the Appendix A (Figure A.

10-Figure A. 11).

During experiments partial evaporation of methanol (MeOH) and methyl

propionate (MeP) occurred. Being able to quantify the amount of MeOH and

MeP in the gas phase directly, under different operating conditions, was

essential in order to close the carbon balance of the system and thus validate

our analysis method and the accuracy of the experimental results in general.

For the calibration of GC for methanol in the gas phase, a gas stream of

He/N2 was bubbled through a flask of 100ml, almost full with MeOH, that

was placed inside a cooling bath for controlling the temperature. The gas

stream (He/N2/vapour MeOH) was analysed by GC using the method

described (Table A. 13). Nitrogen was used as internal standard and based

on the change of its peak area before and after passing the flask, the amount

of MeOH in the gas phase was calculated. For this purpose, the GC was first

calibrated for N2 using N2-He mixtures for a concentration range 5-40% v/v

N2-He (Figure A. 12, Appendix A). During the calibration of vapour MeOH,

2ml20oC,1bar/min of 30%v/v N2:He stream was introduced in the inlet so that

the change of N2 peak area would be easily observed. In addition, this

experiment was conducted in a range of temperatures (5-20oC). In all cases

the temperature in the cooling bath was lower than the ambient temperature

to avoid any downstream condensation of vapour MeOH.

The fraction of a component i (MeOH, MeP) in the gas phase, , can be

calculated based on (A.6),

(A.6)

where, is the activity coefficient of component i and shows the deviation

from the Raoult’s law for ideal mixtures, is the fraction of i in the liquid

phase. During the calibration pure MeOH was used and therefore

and . In all cases, the pressure in the container, PTOTAL, was equal to

iy

( )v

i i ii TOTAL

x P Ty

P

i

ix

1MeOHx

1MeOH


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1.06bara using a pressure sensor (up to 2bar). The vapour pressure of MeOH,

, was calculated based on Antoine equation,

(A.7)

where in the case of methanol, A= 5.20277, B= 1580.08 and C= 239.5 for

temperature between 263-356K [205].

Based on the above equations the theoretically expected fraction of MeOH in

the gas phase in different temperature conditions was calculated (Table A.

14).

Table A. 14 Theoretical vapour pressure and methanol fraction in the gas phase for a range of temperature conditions, calculated from Antoine’s

equation (A.7).

T (K) PvMeOH (bar) yMeOH

278.15 0.054 0.052

283.15 0.072 0.069

288.15 0.098 0.092

293.15 0.13 0.12

The corresponding experimental results of yMeOH are shown in Figure A. 39,

where they are also compared with the theoretically expected values of Table

A. 14. It can be seen that there is excellent agreement in all temperatures, fact

that indicates the validity of the calibration method. The GC calibration plot

for methanol in the gas phase is given in the Appendix A in Figure A. 13.

v

MeOHP

log ( )( )

v

MeOH o

BP bar A

C T C


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Figure A. 39 Experimental and theoretical values of methanol fraction in the gas phase for different temperature conditions.

Similarly, for GC calibration for MeP in the gas phase the same procedure

was followed but in this case a flask of 100ml almost full with MeP was used.

The vapour pressure of MeP, 𝑃𝑀𝑒𝑃𝑣 in bar, was calculated based on (A.9),

where in the case of MeP, A= 3.98745, B= 1129.57 and C= 204.24 for

temperatures between 267-375K [205]. Based on (A.6) the theoretically

expected fraction of MeP in the gas phase in different temperature conditions

was calculated (Table A. 15). The experimental results of yMeP and their

comparison with the corresponding theoretical values of Table A. 15 are

shown in Figure A. 40.

Table A. 15 Theoretical vapour pressure and methyl propionate fraction in the gas phase for a range of temperature conditions, calculated from

Antoine’s equation (A.7).

T (K) PvMeP (bar) yMeP

278.15 0.039 0.037

283.15 0.052 0.049

288.15 0.0684 0.065

293.15 0.0892 0.084


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Figure A. 40 Experimental and theoretical values of methyl propionate fraction in the gas phase for different temperature conditions.

It can be seen that again there is good agreement in all cases. The calibration

plot for MeP in the gas phase is given in the Appendix in Figure A. 14.


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4. Liquid phase analysis

For the liquid analysis a mid-polar capillary column (DB-624, 30m x 320μm x

0.25m, Agilent,) was used. In addition, a 2m long guard column of the same

material with the main column was added before the main column to protect

it from the acidic nature of the liquid samples. The liquid samples were

injected by an auto injector and analysed by means of a FID detector.

The developed GC method for the analysis of MeOH/MeP mixtures is

shown in Table A. 16. A typical chromatograph of liquid analysis is shown in

Figure A. 41, where it is clear that the peaks are well separated, quite sharp

and the total analysis takes no more than 3min. The reproducibility of the

analysis was satisfactory as evidenced by analysing the same sample several

times. The relative standard deviation for the liquid analysis was less than

2%.

Table A. 16 GC operating conditions for the liquid analysis of the methoxycarbonylation of ethylene.

Column Name DB-624

Split Flow 100:1

Column Flow 10ml/min

Oven Temperature 190oC (3min hold)

Detector FID

H2 flowrate 30ml/min

Air flowrate 400ml/min

Front Signal Frequency 50Hz/0.004min


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Figure A. 41 A typical chromatograph of the liquid analysis of a MeOH:MeP mixture of 80:20%w/w.

For the GC calibration for methanol and methyl propionate in the liquid

mixture, mixtures of them in different compositions were prepared. It should

be noted that this binary system deviates from the behaviour of an ideal

liquid mixture. Therefore, in order to prepare well-defined MeOH-MeP

mixtures, the density and the mass fraction of the mixtures should be

expressed as a function of the volume of MeOH added during the mixture

preparation. For this purpose, volumetric flasks of 5ml were used and in

each of them different volume of MeOH was added. Then, the flask was

filled up to 5ml with MeP and the weight of the flask was measured in a

balance with accuracy ± 0.0001g. The required MeOH volume added for the

preparation of a 5ml MeOH-MeP solution with certain mass fraction and the

corresponding density of the mixture are shown in Figure A. 42 and Figure

A. 43 respectively.

MeOH

MeP


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Figure A. 42 Required methanol volume for the preparation of a 5ml methanol:methyl propionate mixture with certain mass fraction.

Figure A. 43 Density of methanol:methyl propionate mixtures as a function of their mass fraction.

The GC was calibrated for the analysis of liquid MeOH: MeP mixtures with

concentrations that ranged between MeOH:MeP=40:60-10:90%w/w. The

mixtures were prepared in a fume cupboard using two pipettes of 1ml. The

GC calibration plots for MeOH and MeP are shown in the Appendix A in

Figure A. 15 and Figure A. 16 respectively.


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5. Catalyst preparation and oxygen effect on catalyst deactivation

Initial experiments showed no reaction occurring, indicating that something

was making the catalyst inactive. Over a year was spent investigating the

possible sources of this problem. Firstly, the hypothesis that the catalyst is

deactivated along the flow set-up, hence some parts of the set-up are

responsible for the deactivation, was tested. In order to investigate for

surface effects in the reactor, various reactors with different materials were

tested such as Stainless Steel, SilcoSteel, Titanium, Hastelloy but no

difference on catalyst activity was observed with total absence of reaction. In

addition, many other parts of the set-up (e.g pump’s syringe, separator,

filters, O-rings) were bypassed or replaced to investigate if they are causing

catalyst deactivation. No reaction was observed in any case indicating an

inactive catalyst. Numerous standard experiments were performed under

different operating conditions, rig configurations reactor types and ways of

introducing the fluids. However, none of the modifications resulted to a

noticeable difference on the reaction rate; no methanol conversion was

observed in any case.

After all these tests, there was great confidence that it is not the set-up that

deactivates the catalyst. Next hypothesis that was tested was that the catalyst

batch used is inactive. For this reason, different catalyst batches of the same

and of different concentrations were tried. It was found that using very

concentrated catalyst solutions reaction was happening but in significantly

less extent than expected. Hence, it was deduced that a portion of the

catalyst was deactivated and the only left hypothesis was that this happens

during the preparation of the feed mixture where the catalyst is being

diluted with methanol and methyl propionate to the desired concentration.

To investigate this hypothesis, various standard experiments were

conducted using different catalyst concentration in the feed. The operating

conditions of a standard experiment were a gas feed of 10%v/v CO:C2H4


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with a flowrate of 0.2ml25oC,10bara/min and a liquid composition of 30%wt.

MeOH:MeP with a flowrate of 0.005ml/min at 100oC and 10bar(absolute).

In Figure A. 44, the reaction rate versus catalyst concentration curve does not

pass through the origin as expected, showing that zero reaction rate is

observed for a non-zero catalyst concentration. This indicates that ca.

3 ∙ 10−4 𝑚𝑜𝑙 𝐿⁄ of catalyst was deactivated which corresponds to ca. 34ppm

Palladium. This explains why with the standard catalytic solution that

contains only 14ppm Palladium we couldn’t observe any reaction. A portion

of the catalyst was deactivated during the feed preparation. It is worth

noting that the actual amount of Palladium species deactivated is very small,

however because in our microsystem very small amount of catalyst are

required, this amount becomes significant.

Figure A. 44 Observed reaction rate under standard conditions against catalyst concentration in the feed for preparation of the catalytic mixture under air

atmosphere.

It was found that the catalyst deactivation was happening during the

preparation of the feed mixture (dilution of cat. mixture with methanol and

methyl propionate) under air atmosphere. More specifically, oxygen from

the atmosphere dissolved in the liquid mixture, was oxidising and

deactivating the catalyst. This was also supported by 31P NMR analysis of a


Page 250

typical feed catalytic mixture (Figure A. 45) where many more peaks

(possibly of oxidised species) appear than the two expected of the

protonated ligand and the active catalyst at 45ppm and 69ppm respectively.

Figure A. 45 31P NMR spectrogram of typical feed catalytic mixture.

Instead, when degasing methanol and methyl propionate with argon and

then preparing the feed mixture in a glove box under argon atmosphere, and

studying again the effect of catalyst concentration on the reaction rate, the

results were very different (Figure A. 46). Now, the effect of catalyst

concentration is as expected, with the reaction rate versus catalyst

concentration curve passing through the origin, indicating no catalyst

deactivation.


Page 251

Figure A. 46 Observed reaction rate under standard conditions against catalyst concentration in the feed for preparation of the catalytic mixture under argon

atmosphere.

In conclusion, it was found that oxygen of the atmosphere was deactivating

the catalyst when preparing the feed mixture under air atmosphere. For this

reason, the liquid feed preparation for all the experiments of the kinetic

study was done in a glove box under argon atmosphere to prevent any

catalyst deactivation. Standard experiments were also regularly performed

to validate the stability of the catalyst activity.


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6. Reactor pretreatment section

An ethylene pretreatment section was installed upstream of the reactor

which consisted of a 2m long Hastelloy tubing with 1.75mm inner diameter.

In the pretreatment section the MeOH:MeP liquid solution was mixed with

ethylene at 100oC at 10bara. The residence time of the liquid was ca. 30min.

In this step, ethylene binds with catalyst, protecting it from contact with a

flow rich in carbon monoxide that could poison and possibly deactivate the

catalyst. This is suggested based on previous studies in autoclaves reactors

by Lucite International.

7. Reactor design

Choosing the material of the reactor is a crucial aspect when designing a

reactor. The ideal reactor material is inert and does not interact with any of

the reactants, products or the catalyst and remains inert over time. For this

reason, the first choice was a fluoropolymer (PFA) capillary, known for its

inert nature. The capillary was coiled on a spiral plate (Figure A. 47) which is

useful for flow observation.

Figure A. 47 Spiral plate with PFA capillary reactor.

To ensure that the reaction inside the PFA reactor on the spiral plate will be

at isothermal conditions, the temperature gradient was measured in both


Page 253

radial direction and along the thickness of the plate for a range of

temperatures. In order to measure the temperature gradient in the radial

direction, two holes with different depths (d1, d2 with d1<d2) were drilled on

the metallic plate and the temperature was measured by means of two

thermocouples. The temperature measurements are shown in Table A. 17.

The temperature gradient is less than 0.2oC in all cases which is insignificant.

Table A. 17 Temperature gradient in the radial direction of the spiral plate for a range of temperatures.

Thermocouple 1 (d1)

T (oC)

Thermocouple 2 (d2)

T (oC)

76 76.1

85.4 85.6

94.8 94.9

104.1 104.2

113.3 113.5

To determine the temperature gradient along the thickness of the plate, the

temperature was measured in a few different points for a wide range of

temperatures. These points are the bottom of the metallic plate of the reactor,

the bottom and the top of the capillary and the bottom and the top of the

acrylic plate, installed on top for better insulation (Figure A. 48). The

temperature was measured by means of thin thermocouples with thickness

equal with 250μm.

Figure A. 48 Layers of spiral plate with capillary reactor.

In Table A. 18 the temperature measurements are shown. The temperature

difference in the bottom and the top of the capillary is always less than 0.5oC.

Hence, the reactor can be considered isothermal.


Page 254

Table A. 18 Temperature gradient at different points of the spiral reactor.

T (oC)

Bottom of

metallic plate

Bottom of

capillary

Top of

capillary

Bottom of

acrylic plate

Top of

acrylic plate

66 65.2 64.9 53.5 44.6

86.1 84.7 84.2 68.1 51.9

107.2 105.4 104.7 83.5 63.4

128.1 125.2 124.2 100.7 80.1

Next step was to perform blank experiments (without catalyst in the feed)

with this PFA spiral reactor to ensure satisfactory operation. However, blank

experiments showed that at high temperature the mole balance of ethylene

between the inlet and the outlet of the system did not close. Instead, analysis

showed that ethylene concentration significantly decreased in the outlet, but

only when the temperature was high. Accuracy of vapour-liquid equilibrium

of the system and of the analysis methods were examined, but none of this

was the answer. Finally, tubing permeability was found to be the reason for

the mole balance discrepancy.

Permeability experiments

The permeability of the PFA reactor was tested at two temperature

conditions (25oC, 100oC) by pressurising the system at 10bara with a gas

mixture of CO:C2H4=1:9v/v and analysing the exiting gas stream in terms of

composition and volumetric flowrate (at 25oC, 1bara). The composition of

the exiting stream was analysed by GC and its volumetric flowrate was

measured by a bubble meter. No liquid was flowing through the system,

hence no reaction was taking in this experiment.

In Figure A. 49 the molar flowrate of carbon monoxide and ethylene are

shown in the exit of the PFA reactor for two reactor’s temperatures.


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Figure A. 49 Molar flowrate of carbon monoxide and ethylene in the outlet (25oC, 1bara) of a PFA tubing using an inlet gas mixture of CO:C2H4=1:9v/v and reactor’s

conditions 25oC and 100oC at 10bara.

At 25oC the molar flowrate of carbon monoxide and ethylene in the outlet of

the reactor is equal with that in the inlet. However, when increasing the

temperature in the PFA tubing from 25oC to 100oC, ethylene molar flowrate

decreases by 29% compared to the inlet. For carbon monoxide the decrease is

very small and within the experimental error. Therefore, the tubing is

permeable to ethylene at elevated temperature and thus this material cannot

be used for the kinetic study of the MeP system.

The same procedure was followed using other fluoropolymer tubings such

as ETFE, PEEK and Halar ECTFE but all of them presented the same

behaviour as the PFA tubing, permeable to ethylene at elevated temperature.

Hence it was concluded that no fluoropolymer tubing is suitable for the

kinetic study of the MeP system.

Hastelloy tubing was tested for its permeability following the same

procedure as before. In Figure A. 50 the molar flowrate of carbon monoxide

and ethylene are shown in the exit of the Hastelloy reactor for two reactor’s

temperatures.


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Figure A. 50 Molar flowrate of carbon monoxide and ethylene in the outlet (25oC, 1bara) of a Hastelloy tubing using an inlet gas mixture of CO:C2H4=1:9v/v and

reactor’s conditions 25oC and 100oC at 10bara.

The molar flowrate of carbon monoxide and ethylene in the outlet of the

Hastelloy reactor found equal to the inlet ones for both temperatures. No

significant change was observed in the molar flowrates of carbon monoxide

and ethylene at any temperature indicating no permeability of the gases

through Hastelloy.

The same procedure was followed using other metal tubings such as

Titanium, Stainless Steel and SilcoSteel and none of them found permeable to

carbon monoxide or ethylene at elevated temperatures, hence they are all

suitable for the kinetic study of the MeP system.

Isothermality

Preliminary calculations of the temperature profiles along the capillary

reactor were performed in order to investigate if the thermal entry length is

significant and if the length to temperature stabilisation is comparable to the

total length of the reactor. Single phase flow was considered for ease of the

calculations and specifically methanol flowing in PTFE tubing with 1mm

inner diameter. PTFE was chosen as it is the least conductive material (hence


Page 257

the worst case scenario). It has smaller thermal conductivity compared to

metal tubing (0.25W/m∙K compared to 16W/m∙K for stainless steel). Two

flowrates were tested, 0.005ml/min and 0.2ml/min which correspond to

typical liquid and gas flowrate respectively during this study.

The solution of the energy balance of a single phase flow along a circular

pipe considering two resistances, the fluid convection and the tubing

conduction, for constant temperature on the walls is given by (A.8) and (A.9)

[206],

𝑇𝑠 − 𝑇𝑚(𝑥)

𝑇𝑠 − 𝑇𝑚,0= 𝑒𝑥𝑝 (−

1

�̇� ∙ 𝐶𝑝 ∙ 𝑅𝑡𝑜𝑡) (A.8)

𝑅𝑡𝑜𝑡 =ln (

𝑂𝐷𝐼𝐷

)

2 ∙ 𝜋 ∙ 𝑥 ∙ 𝑘+

1

ℎ̅ ∙ 2 ∙ 𝜋 ∙ 𝐼𝐷 ∙ 𝑥 (A.9)

where Ts and Tm is the walls and the mean temperature (K) respectively, �̇� is

the mass flowrate of the fluid (kg/s), Cp is the specific heat of the fluid

(J/kgK), OD and ID are the outer and the inner diameter of the tubing, x is

the distance (cm) in the axial coordinate, ℎ̅ is the heat transfer coefficient of

the fluid (W/m2K) and k the thermal conductivity of the tubing (W/mK).

The heat transfer coefficient of the fluid is calculated based on (A.10),

𝑁𝑢̅̅ ̅̅

𝐷 =ℎ̅ ∙ 𝐼𝐷

𝑘 (A.10)

assuming laminar flow in a straight, smooth pipe.

It was found that the centre of the tubing reaches rises from 293K to 373K

(typical reaction temperature) in less than 1mm when flowrate is

0.005ml/min and 1.5cm when flowrate is 0.2ml/min, which is insignificant

compared to the total reactor length (6m). These results were validated with

Comsol simulations (Figure A. 51-Figure A. 52), where a simplified scenario

was tested for ease of calculations. Specifically, the temperature profile of a

single phase flow (only methanol) was tested along the reactor, a PTFE

tubing, rising from 293K in the feed to 373K (typical reaction temperature).


Page 258

Two simulations were considered for two liquid flowrates at 0.005ml/min

and 0.2ml/min typical for the liquid and the gas flowrates.

Figure A. 51 Temperature profile in axial direction for single phase flow (MeOH only) with 0.005ml/min in a PTFE tubing with 1mm inner diameter at atmospheric

pressure and room temperature in the inlet.


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Figure A. 52 Temperature profile in axial direction for single phase flow (MeOH only) with 0.2ml/min in a PTFE tubing with 1mm inner diameter at atmospheric

pressure and room temperature in the inlet.

Although the simulation case is a simplified case, it is still representative and

indicates that reactor reaches reaction temperature so quickly that entrance

effects can be neglected. This is mainly because of the small tubing diameter,

the thin tubing walls and the slow flow.

Blank experiment

A series of blank experiments were performed to ensure that the capillary

internal surface is inert and is not interacting with any of the components of

the system. The blank experiments were conducted at 100oC, at 10bar with a

gas feed mixture of CO:C2H4 (1:9 v/v, υg=2ml299K,1bar/min) and a liquid feed

mixture of 30:70 w/w% MeOH:MeP (with no catalyst, υℓ=0.01ml/min). In

Figure A. 53 the molar flowrates in the inlet and the outlet of the reactor are

shown for all components using a Hastelloy reactor with 1mm inner

diameter. The molar flowrates were calculated based on GC analysis of the

gas and liquid phase in the inlet and outlet of the reactor.


Page 260

Figure A. 53 Molar flowrates of all components in the inlet and the outlet of a Hastelloy capillary reactor during a blank experiment.

There is no significant change in the molar flowrates of any of the

components between the inlet and the outlet indicating that there is no

interaction with the reactor’s surface and hence the Hastelloy reactor is

suitable for our kinetic study. Same inert behaviour was also observed with

all other metal tubings used such as Titanium, Stainless and SilcoSteel.

However, Hastelloy was the final choice of the reactor material, as it is also

used industrially for the same process and has presented excellent stability

over time.

Standard experiment

A standard experiment was performed in order to check that the carbon

balance closes and hence that the analysis methodology is accurate for the

kinetic study. Standard experiments were repeated regularly in order to

ensure that the activity of the catalyst remained constant. The standard

experiment was conducted at 373.15K, at 10bara using a 6m long Hastelloy

reactor with 1mm inner diameter. A gas mixture of CO:C2H4 (1:7 v/v,

υg=1.8ml298K,1bar/min) and a liquid mixture of 30:70 w/w% MeOH:MeP

(υℓ=0.005ml/min) were used in the feed. The results of the standard


Page 261

experiment are shown in Figure A. 54, where the molar flowrates of all

components are shown in the inlet and the outlet of the reactor.

Figure A. 54 Molar flowrates of all components in the inlet and outlet of the reactor for a standard experiment in a Hastelloy reactor.

Based on the results of the standard experiment the mole balances of all

components of the system were calculated and are presented in Table A. 19.

Table A. 19 Mole balance of MeP system for standard experiment.

mol/min Inlet Outlet Mole

Difference

% Mole

Difference

MeOH 6.77E-05 6.58E-05 -1.90E-06 2.8

MeP 6.61E-05 6.8E-05 1.92E-06 2.9

CO 8.27E-06 7.19E-06 -1.08E-06 13

C2H4 4.96E-05 4.75E-05 -2.03E-06 4.1

Mole differences of all components are very close to each other indicating a

good carbon balance. Specifically the carbon balance closed within 3%

difference. This validates the accuracy of the analysis methods used and

proves that this experimental configuration is well defined and hence very

suitable for kinetic studies.


Page 262

8. Separator design

Following the reactor, the reaction is quenched due to the drop of the

temperature and the gas-liquid mixture enters a separator. Two different

designs of gas-liquid separators were tested for this purpose. Firstly, a glass

microseparator (mikroglas) used for the experiments with the model reaction

(Chapter 3.3.1.2) could be used for our kinetic study as the manufacturer

specified that it can stand up to 15bara while our study will take place at

10bara. This was also tested experimentally and was found that the

microseparator can withstand pressures up to 13bar without any problem.

Significant amount of time was spent testing further the microseparator, but

it was found that its operational window is very small and it is almost not

feasible to use it in our case. This is because the pressure difference required

to apply across the microseparator for a successful and stable separation was

found to be 0.01-0.02bar. When a higher pressure difference was applied gas

was breaking through to the liquid outlet while for a smaller pressure

difference liquid was escaping to the gas side. The required pressure

difference (0.01-0.02bar) is proportionally very small for a high pressure

system like ours where the total pressure is 10bara; it is only 1% of the total

pressure. This means that even a very small pressure fluctuation of 1% of the

total pressure can affect the stability of the separation.

A custom-made stainless steel (SS) gravity-based separator of 3ml internal

volume was tested which was made with stainless steel tube, a tee-junction

and a few stainless steel fittings. A schematic of this simple high-pressure

separator is shown in Figure A. 55.


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Figure A. 55 Stainless steel gas-liquid high-pressure separator based on gravity.

The separator was tested successfully with a N2/water mixture at 12bar

(absolute). In the bottom of the separator a metering valve was added in

order to have a smoother liquid sampling without any sudden pressure

drop.

9. Tracer effect on RTD experiments

For the step-change of the liquid feed concentration, ideal tracers would be

chemical components that are already present in the reaction system such as

methanol, methyl propionate or mixtures of them. In this way the system

won’t be disturbed as it would if a completely different chemical was used

for the step change. In addition, due to the fact that the sensors are

integrated with the set-up for the kinetic study, the hydrodynamic study of

the system can be conducted simultaneously with the kinetic experiments,

after every run.

A series of RTD experiments were conducted to investigate the effect of the

tracer choice on RTD parameters such as the liquid residence time, the

dispersion factor and the void fraction. Ideally, the solvent should not affect

these results. Four different tracers were tried (pure MeOH,

MeOH:MeP=70:30%wt, MeOH:MeP=50:50%wt, pure MeP) at certain gas

(CO:C2H4=1:9) and liquid (MeOH:MeP=30:70%wt) flowrates (Table A. 20) at


Page 264

373K, 10bar. It should be noted that the typical liquid concentration in the

feed during the kinetic study was 30:70%wt. MeOH:MeP. The Hastelloy

reactor used had an internal diameter of 1mm and 6m length.

In Table A. 20 the flowrates in the feed of the set-up and the reactor inlet are

shown where different temperature conditions apply. In the feed of the set-

up the flowrates were based on the set values of the mass flow controllers

(after correction for the temperature and the pressure) and the syringe

pump. In the reactor the compositions of the gas and the liquid stream

change due to the change in the temperature. For example methanol and

methyl propionate evaporate resulting to an increase of the gas flowrate. To

take into account this vapour-liquid equilibrium (VLE) effect, a VLE model

was utilised that is able to predict the new compositions and flowrates in the

reactor (100oC) when knowing the corresponding compositions and

flowrates in the feed (25oC). More information about the VLE model can be

found later in Appendix J. The VLE effect is another reason why it is

important to study the hydrodynamics of the system under reaction

conditions.

Table A. 20 Gas and liquid flowrates and gas to liquid ratio in the feed of the set-up and under reaction conditions.

Feed of set-up

299K, 10bar

Reactor Inlet

373K, 10bar

υg (ml/min) 0.2 0.277

υℓ (ml/min) 0.01 0.0083

g/ℓ ratio 20 33

For these flowrates, the observed flow pattern (by means of a microscope) in

the feed of the set-up (25oC, 10bara) where the tubing was transparent (made

of PFA with same inner diameter) was slug-annular flow with elongated

bubbles (Lbubble>30cm) and relatively short liquid slugs (Lslug<2mm). Under

reaction conditions (100oC, 10bara) it is expected to have a more annular-like

flow pattern due to the increase of the gas flowrate and the decrease of the


Page 265

liquid flowrate (as liquid evaporates when temperature increases). It was

though not feasible to observe the temperature effect experimentally. The

reactor was made of Hastelloy which was not transparent.

The analysis of the RTD experiments was based on the assumption that the

inlet signal was a perfect step and therefore no deconvolution of the data is

needed. This assumption enables a quicker and simpler data analysis and in

the same time it was found that affect only slightly our results. Concerning

the liquid residence time measurement it was found that this assumption

causes small error in our findings of less than 10%. Due to this simplification,

the real dispersion factor would be slightly smaller than the one calculated,

due to upstream dispersion that was not excluded. Hence in this way we

establish the worst case scenario.

The results of the RTD experiments with different tracers are shown inTable

A. 21, where τℓ is the experimentally measured liquid residence time, D/uL

is the dispersion number that found by comparison of the RTD curves with

corresponding curves in the literature [8]. A sample demonstration of the

analysis of the RTD signal can be found in Appendix D.

Table A. 21 Effect of solvent of the step-change on the RTD results.

Tracer

Mean liquid

residence time, τℓ

(s)

Dispersion

number,

D/uL

Void

fraction

prefactor A

Pure MeOH 1829 0.006 ± 0.001 0.956

70:30%wt.MeOH:MeP 1835 0.0065 ± 0.001 0.956

50:50%wt.MeOH:MeP 1880 0.012 ± 0.001 0.955

Pure MeP 1910 0.0148 ± 0.001 0.949

The last column in Table A. 21 corresponds to the numerical prefactor, A,

found to satisfy (A.11) and (A.12). It should be reminded here that for the

most common hydrodynamic correlations, Armand’s model and

homogenous model A=0.833 and A=1 respectively.


Page 266

(A.11)

(A.12)

The residence time is not affected significantly by the choice of the tracer.

The dispersion number however increases slightly when the tracer is more

concentrated with MeP. This is due to the decreased viscosity of the solution

in that case, which results to a thinner liquid film around the bubbles and

hence a larger dispersion number [174,184]. However, the dispersion number

in all cases is small, hence the flow can be considered to satisfy plug flow

criterion (D/uL<0.01).

The tracer does not affect the void fraction prefactor significantly. Prefactor

value is between the corresponding value of Armand’s and homogenous

model (closer to the later one), hence none of these model is predictive in this

case. This may be due to the fact that in these studies [70-72,76,78] different

gas-liquid systems were studied, hence the liquid film thickness (which

affects largely the prefactor A) was different due to the different liquid

properties. This fact highlights the necessity of conducting RTD experiments

for the determination of the void fraction and not following one of the

existing models.

After confirming that the choice of the tracer for the step change is not

affecting the hydrodynamic results, pure methanol was chosen for the rest of

the RTD experiments.

10. Characterisation of the mass transfer characteristics of the system

Another crucial aspect in a kinetic study of a system is to ensure that there

are no mass transfer limitations based on Hatta criterion,

1g

g

jA

j j

L

j


Page 267

𝐻𝑎 =

√𝑘𝑟∙𝐷𝐴ℓ

𝑘ℓ < 0.3

(A.13)

where is the reaction rate constant of the reaction, is the

reactant A diffusivity into the liquid and the mass transfer

coefficient of A in the liquid phase.

There are several hydrodynamic models available in the literature for the

calculation of the mass transfer coefficient, kℓα, in a system (Chapter 2.3.2).

Using four of them Hatta number was calculated for the cases A (Table 5-1)

and the results are shown in Table A. 22. It was assumed that the reaction

rate constant is equal to 7·10-5s-1 (based on previous, preliminary studies on

the MeP system), the diffusivity equal to 9·10-9 m2s-1 (based on the

diffusivities of carbon monoxide and ethylene in methanol at elevated

temperature, [207,208]) and the film thickness equal to 19μm based on RTD

results. The flow characteristics of the system were based on flow

observation at 25oC. At reaction temperature (100oC) the bubble length is

expected to be even larger and the liquid slug smaller due to evaporation of

the liquid phase.

In Table A. 22, it is shown that all models except Yue et al. model give

similar results. Yue model results to significantly higher Hatta numbers,

probably because of the use of rectangular channels, but still in that case

Hatta numbers are below the limit for the kinetic control.

Table A. 22 Hatta number for case A based on various mass transfer models.

Mass transfer model 𝒌𝓵𝜶 (s-1) 𝒌𝓵 (m/s) Hatta number

Bercic and Pintar [102] 0.053 0.0013 5.93∙10-4

van Baten [105]

(only film contribution) 11.46 0.0016 4.91∙10-4

Yue [99] 0.199 0.000028 0.028

Sun [209] 16.3 0.0023 3.45∙10-4

1( )rk s 2( )AlD m s

( )lk m s


Page 268

It was concluded that in the range of flowrates we are planning to work,

MeP system will operate under kinetic control as Hatta number is well below

the kinetic control criterion (Ha<0.3).

11. Vapour-liquid equilibrium model

A VLE model developed by Torres [210] for the same gas-liquid system was

used and will be described in brief here. In Figure A. 56 the equilibrium

block is shown, where knowing the initial compositions in the inlet, it is

possible to calculate the compositions of the gas and the liquid phase in a

new equilibrium position by means of a vapour-liquid equilibrium model.

Figure A. 56 Study block for vapour-liquid equilibrium model.

The mole balance in the equilibrium block is shown in (A.14),

(A.14)

where, are the fractions of component i in the liquid and in the gas

phase respectively, while are the total molar flowrates in the

liquid and in the gas phase respectively. The summation of the fractions in

the liquid and in the gas phase should be equal to 1.

(A.15)

(A.16)

For the calculation of the composition in the equilibrium block, the

equilibrium equations are also needed. For components that are very dilute

, , , ,

in in in in eq eq eq eq

i total i g total i total i g totalx F y F x F y F

,i ix y

, ,,total g totalF F

1ix

1iy


Page 269

in the liquid phase (xi<0.1) such as carbon monoxide and ethylene, Henry’s

law can be applied,

(A.17)

where is the fugacity coefficient of component i in the gas phase, P is the

total pressure of the system, is the activity coefficient of component i in

the liquid phase (determined by UNIQUAC equation) and is the

Henry’s constant for the component i in the liquid mixture after correction

for the elevated pressure (Poynting factor). For the rest of the components

(methanol, methyl propionate) the following equilibrium equation can be

used,

(A.18)

where is the vapour pressure of component i determined by Antoine

equation.

More details for the equations and the constants used for the calculation of

, , , can be found in Torres thesis [210]. The model was

written in gPROMS modelling software and the solvers used for the

initialisation and for the block solution are BDNLSOL and SPARSE

respectively. The model is presented analytically in Appendix E.

There is only one modification made in our case on the equations listed in

Torres thesis that should be noted. This is for the calculation of the pure

component saturated volume, , necessary for calculation of the fugacity

constant, . The original equation (Torres thesis, p.250, eq. 1.36) is shown

below,

(A.19)

where Tc, Pc are the critical temperature and pressure of each component

respectively, Tr is the dimensionless critical temperature of each

,v mix p

i i i i iy P x He

v

i

i

,mix p

iHe

v vap

i i i i iy P x P

vap

iP

v

i i,mix p

iHe vap

iP

V

v

i

2/71 1 rT

RA

c

c

R T ZV

P

cT T


Page 270

component and is the Rackett compressibility factor. The problem

appears when trying to use (A.19) for carbon monoxide and ethylene. Their

critical temperatures (132.92K and 282.34K respectively) are well below the

experimentally operating temperature (295-390K) resulting to a negative (1-

Tr) term. The problem is that mathematically is not permitted to raise a

negative number to a non-integer number (2/7) and therefore gPROMS

crashes when faces this calculation. An arbitrary modification of (A.19) was

made to overcome this problem and is shown in (A.20),

(A.20)

In order to validate that the VLE model was correctly transferred in

gPROMS, that the modification made does not affect its accuracy and that

the constants used are the correct ones, a validation of the model was

performed by comparing its predictions by previous experimental data of

Torres [210]. Simulations were performed for an inlet gas stream of

xC2H4:xCO=5:1 and a liquid stream of 30:70 wt.% MeOH:MeP. The

temperature considered in the equilibrium block was 363K while the

equilibrium pressure were between 3-18bar.

In Figure A. 57-Figure A. 59 the fraction of the components in the gas and the

liquid phase are shown respectively against different pressure conditions in

the equilibrium block.

RAZ

2/71 1rT

RA

c

c

R T ZV

P


Page 271

Figure A. 57 VLE model predictions for gas fraction of all components against pressure at 363K.

The VLE model predictions both for the gas and the liquid fractions are in

excellent agreement with Torres results, especially for the pressure range we

are interested in, between 8-12bar.

Figure A. 58 VLE model predictions for liquid fraction of carbon monoxide against pressure at 363K.


Page 272

Figure A. 59 VLE model predictions for liquid fraction of carbon monoxide against pressure at 363K.

This model will allow to determine the compositions in the inlet and outlet

of the reactor at reaction conditions based on experimentally known

compositions in the inlet and outlet of the set-up (T=ambient,

P=atmospheric).


Page 273

12. Conversion data for kinetic experiments of Chapter 5

Table A. 23 Operating conditions and methanol conversion for kinetics experiments presented in Chapter 5.

P bara

T K

Inlet yCO

Inlet yC2H4

Inlet yHe

%wt. MeOH Pd mol/m3

XMeOH %

10 100 0.126 0.5 0.45 31.8 1.30E-03 9.07 10 100 0.332 0.5 0.168 31.8 1.30E-03 18.54 10 100 0.23 0.5 0.27 31.8 1.30E-03 14 10 100 0.426 0.5 0.074 31.8 1.30E-03 19.3 10 100 0.096 0.5 0.404 31.8 1.30E-03 7.1 10 100 0.1 0.9 0 31.8 1.30E-03 9.63 10 100 0.1 0.9 0 80 1.30E-03 3.4 10 100 0.1 0.9 0 20.9 1.30E-03 10.89 10 88 0.1 0.9 0 30 2.82E-04 6.82 10 94 0.1 0.9 0 30 2.82E-04 7.6 10 100 0.1 0.9 0 30 2.82E-04 6.4 10 106 0.1 0.9 0 30 2.82E-04 6.8 10 111 0.1 0.9 0 30 2.82E-04 6.2 10 100 0.1 0.709 0.191 31.8 1.30E-03 7.89 10 100 0.1 0.529 0.371 31.8 1.30E-03 7.1 10 100 0.1 0.465 0.435 31.8 1.30E-03 5.33 10 100 0.1 0.35 0.55 31.8 1.30E-03 4.55 10 100 0.1 0.83 0.07 31.8 1.30E-03 8.88 10 100 0.1 0.4 0.5 31.8 1.30E-03 6.71 10 100 0.1 0.235 0.665 31.8 1.30E-03 5.1 10 100 0.1 0.64 0.26 31.8 1.30E-03 7.6

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Kinetic studies of gas-liquid reactions in capillary ......Declaration of Authorship I, Chara Psyrraki, declare that this thesis titled ‘Kinetics of gas-liquid reactions in capillary